January 18, 2021 1:39 PM EST

Maryanne Larrea, a young devotee of President Donald Trump, felt the sting of tear gas for the first time in her life on Jan. 6, when she marched among the crowd that Trump incited to storm the Capitol. A gun-rights activist and hardline conservative Christian, Larrea, 22, says she did not go inside the building that day; the tear gas was enough to force her away from the front of the mob. But when she got back home to Pennsylvania and started scrolling through reactions to the violence, she realized she might be in trouble.

“Everyone is saying it was a terrorist attack,” she told TIME about a week after the riot. “Everyone thinks I’m a terrorist because I was at that event.”

And it isn’t just the people in her newsfeed. A growing chorus of security experts and politicians has cast the mob, or parts of it, in terms that are typically reserved for ISIS and Al Qaeda. Some commentators have even begun to call for a new American war on terror in response to the Capitol riot, one aimed at President Trump’s more radical supporters on the right.

That has stirred a broader debate about how best to fight right-wing domestic terrorism: with criminal laws already on the books, with new powers modeled on those crafted to fight Islamic terrorism after 9/11; or with some mix of the two. At the same time, it is raising new fears among rights advocates that civil liberties already eroded after 9/11 will be further diminished.

On Wednesday morning, while presiding over Trump’s impeachment in the House, Speaker Nancy Pelosi referred to the rioters as “domestic terrorists,” a phrase that President-elect Joe Biden has also used to describe them. Senate Minority Leader Chuck Schumer has called for them to be put on a “no-fly list” of terrorism suspects, a measure that the FBI said it was “actively looking at.” Even veterans of the Trump Administration have urged the government to unleash the tools of counterterrorism, honed in the two decades since 9/11, against the perpetrators of the Capitol assault, their supporters and their associates.

“It will be a generational challenge for us,” says Elizabeth Neumann, who served for three years under President Trump as the Assistant Secretary of Homeland Security, overseeing counterterrorism and threat prevention. “We have to go after the people doing the incitement, the people who are very serious about doing these attacks, with the same intensity that we did with Al Qaeda.”

Since resigning in April 2020, Neumann has been a vocal critic of the President and his policies. In an interview with TIME, she compared Trump’s role in the Capitol assault to that of Osama bin Laden in 9/11. “This might be a slight overstep,” she says, but for members of the mob that stormed the Capitol, President Trump “was that spiritual leader that bin Laden was for Al Qaeda. He was that face, and that spokesperson, that rallied the troops.”

Such comparisons point to a turn in the debate about terrorism that many security experts have wanted to see for years. According to U.S. government statistics, the majority of deadly extremist incidents in the U.S. are motivated by far-right ideologies, especially white supremacy. Yet the threat of Islamic radicalism commands a far greater share of government resources. Heidi Beirich, former head of the Intelligence Project at the Southern Poverty Law Center, calls this disparity a sign of the “great hypocrisy” on the issue of terrorism in America. “When it comes to white supremacy,” she says, “it is a battle to prove that it is also terrorist violence.”

The Capitol riot seems likely to change that, at least in the short term. But civil liberties advocates have already raised concerns about the cost. Senator Schumer’s call for the FBI to put rioters “immediately” on a no-fly list could violate their right to due process, as the practice often did when aimed at suspected jihadists. “In my view, the government’s terrorism blacklists are a cautionary tale, not a promising model,” Jameel Jaffer, a civil liberties attorney, told the Intercept.

Such notes of concern have been muted in the past week. Few if any of the biggest civil liberties organizations in the U.S. has issued statements urging caution in the rush to find, blacklist or prosecute the Capitol rioters. Speaking to TIME on Thursday, a director at one of these organizations did express concerns “as a private person” about responding to the riot with the tools of counterterrorism. “I do have grave concerns,” he says, asking not to be named, as he was not authorized to speak to the media on this issue. “The war on terror has been done in a way that is not only discriminatory but ineffective. If you are profiling on the basis of characteristics not linked inherently to terrorism, you come out with a whole bunch of problems.”

The dangers lying in the legal gray zone between political speech and incitement to violence are anything but theoretical. Two years into Barack Obama’s presidency, the U.S. launched a Hellfire missile at Anwar al-Awlaki, an American imam who served Al Qaeda as a recruiter. Al-Awlaki’s assassination in Yemen in 2011 remains a stain on Obama’s legacy to many civil liberties defenders, in part because al-Awlaki’s role within the terrorist network was not to commit acts of violence himself. “It was an inspirational job,” says Ali Soufan, a former FBI special agent focused on counterterrorism. “He was instigating.”

Among far-right extremists in the U.S. today, there are countless radicals who play a similar role, preaching violence and hate to their followers behind the shield of Constitutional protections. “The United States today is basically the Mecca of white supremacist ideologues,” Soufan says. And any attempt to silence them will face legal challenges even more complex than the struggle to stop Al Qaeda recruiters, not least because the far right blends so easily among more moderate supporters of the U.S. President.

The words and actions of Trump’s supporters, even when they renounce the results of a free and fair election, or support shows of force from armed militias, are protected by the Constitution, whose First Amendment guarantees free speech and the freedom “peaceably to assemble, and to petition the Government for a redress of grievances.”

Rolling back those freedoms has served in other countries as a prelude to authoritarianism, and it is easy enough to imagine a future U.S. President deciding to label his opponents terrorists before stripping them of their fundamental rights. Throughout his presidency, President Trump attempted to designate Antifa, a loose band of left-wing radicals, as a terrorist organization, a move that civil liberties groups successfully resisted.

Since the assault on the Capitol, the American Civil Liberties Union has taken a different approach, making clear that it will not defend the right to protest in the case of the rioters. “The ACLU has always been about the right to protest, the right to speak,” Jeffrey Robinson, its deputy legal director, said in a panel discussion broadcast on Jan. 8. “This has nothing to do with protest.”

The target of the rioting, Robinson noted, was not a statue or a storefront but the seat of American democracy, a chamber that was in the middle of certifying the results of a presidential election at the moment it was attacked. Among the crowd that took part in the violence, there were dozens of people whose names are already on a government watch list of extremists – the Terrorist Screening Database, a massive catalogue of individuals seen as potential security risks, according to a Washington Post report that cited people familiar with the FBI’s investigation. Vice News reported separately on Thursday that one of the Trump supporters outside the Capitol that day had once served time for fire-bombing an abortion clinic.

Still, among the thousands of people Trump urged to march on the Capitol last week, known extremists and terrorism suspects make up a small fraction. They are even smaller when compared to the President’s base of hardcore supporters. In a YouGov survey published on Wednesday, two thirds of Republicans said that Jan. 6 was a “bad” or “tragic” day for America. But 16% of Republicans said they approve of the takeover of the Capitol.

Larrea, the young Trump supporter, counts herself among this minority, as do many members of her church group. Known as the Rod of Iron Ministries, the group is about as extreme as it gets in their worship of the President and his policies. Based in rural Pennsylvania, they use AR-15 assault rifles in their religious ceremonies, and they believe that Trump’s presidency is a literal godsend for conservative Christians.

The day after the riot, they gathered at the Tommy Gun Warehouse, a massive firearms emporium in the town of Greeley, to take stock of what had happened at the Capitol. “The people at the Capitol signified the people of the world,” Larrea says in summarizing the message of her church leaders. “In a way, we are taking back, the people are taking back the world from the evils of the world. That’s what my congregation has been talking about.”

Under normal circumstances, such a statement would be protected under the First Amendment. But it’s less clear how the U.S. Justice system would respect those protections in the context of a war on domestic terrorism. Neumann, the former DHS official, says people who marched alongside the mob that stormed the Capitol could also find themselves under suspicion, if not also in legal jeopardy. “Who you associate with matters,” Neumann says. “If you don’t want the violence, then don’t provide the cover for the violence.”

By that rationale, virtually everyone who heeded Trump’s call to march on the Capitol could be accused of providing cover for the violence that ensued, and those marchers represent a broad cross section of Trump’s base. According to a TIME analysis of the symbols and flags they carried, the mob included devotees of pro-Trump conspiracy theories like QAnon, as well as neo-Nazis and white supremacists. But some of the calls to punish those involved in the riot have left little room for these distinctions.

“On January 6, terrorists attacked the United States of America,” Rep. Veronica Escobar, a Texas Democrat, said on the House floor before it voted to impeach President Trump on Wednesday. “Those who came and participated must be found and prosecuted,” she said. “Those who aided and abetted must be found and prosecuted.”

From a legal standpoint, this would not be easy. Because there is no law against domestic terrorism on the federal books, the FBI has resorted to some strange legal contortions in their efforts to bring terrorism charges against far-right gangs. In a recent case involving the Boogaloo Bois, an American right-wing extremist group, undercover FBI agents posed as members of Hamas, a foreign terrorist organization, according an indictment issued in November. Only after the two Americans were recorded discussing plans to cooperate with Hamas was the FBI able to charge them with a crime related to terrorism: Conspiracy to provide material support to a designated foreign terrorist organization.

In trying to monitor domestic terrorists, the FBI faces serious legal barriers, says Thomas Warrick, who was the top career counterterrorism official at the Department of Homeland Security from 2008 until 2019. “You could monitor overseas terrorists for what they were saying, even if they hadn’t yet radicalized to violence. Domestically, it’s a different story,” says Warrick, now a fellow at the Atlantic Council. “Constitutional boundaries have to be respected.”

In the wake of the Capitol riot, there has been growing pressure on Congress to empower law enforcement in the fight against far-right extremism. Senator Dick Durbin, an Illinois Democrat, plans to reintroduce the Domestic Terrorism Prevention Act, which passed the House last fall but went nowhere in the Senate. The law would establish new offices at the FBI, the DHS and the Department of Justice dedicated to assessing and countering threats from far-right extremists.

If the Biden Administration wants to take on this threat, it will also need to start designating far-right extremist groups as terrorist organizations, says Soufan, who has long pushed for such designations against neo-Nazi and white supremacist groups.

“They are on par with the jihadis, if not worse,” says Soufan, who was involved in the hunt for bin Laden during his service in the FBI. The response to the Capitol riot reminds him of what happened after 9/11, at least in the way it forced the nation to recognize a threat and respond to it with force. “I look at it as one of these events in our history,” he says, “like Pearl Harbor, like 9/11, that woke up a sleeping giant.”

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