Speaker of the House John Boehner (R-OH) holds a news conference with the newly-elected members of the House GOP leadership at the U.S. Capitol in Washington on Nov. 13, 2014.
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December 3, 2014 5:14 PM EST

Democrats may come to the rescue of House Speaker John Boehner in order to avert a government shutdown next week.

Conservatives are clamoring for the House Republican leadership to use the power of the purse to protest President Barack Obama’s executive order, which could delay deportations for up to five million immigrants who came to the country illegally. Several prominent conservatives, including Texas Republican Senator Ted Cruz and Ohio Rep. Jim Jordan, have rebuked the House Republican leadership’s government funding proposal, but leadership believes enough Democrats will join to pass it, according to a congressional aide.

“I’m waiting to be convinced that it’s a bad idea because on the face of it I think it’s probably the best that we can do right now,” says Democratic Rep. Dan Lipinski of Illinois.

“I think everyone is reluctantly looking at this as probably the most practical solution,” concurs Democratic Rep. John Delaney of Maryland, who is considering voting for Boehner’s proposal. “I do not want to have a government shutdown … If that’s where we end up I don’t think the president should veto it.”

House Democratic Leader Nancy Pelosi opposes the measure, but House Democrats said she hasn’t been whipping against it behind the scenes. Still, several Democrats told TIME they wouldn’t vote for the proposal.

“I hate to give in to their whining,” said Kentucky Democratic Rep. John John Yarmuth of Kentucky, adding that he’ll “probably” vote no. “It doesn’t make any sense to me that we would fund an important agency like that on a piecemeal basis and just having to waste time going through another exercise three months from now.”

The House GOP leadership plan would fund all aspects of the federal government through September 2015, with the exception of the Department of Homeland Security, which would be funded through the next few months. DHS is tasked with carrying out Obama’s executive order. Jennifer Hing, House Appropriations Chairman Hal Rogers’ spokeswoman, said that the language for the bill will be made public “early next week,” which would give little time for conservatives to come up with an alternative.

Conservatives would prefer to have a shorter-term funding solution and some are calling for defunding the programs designated to enact Obama’s executive action.

“That might be something we do closer to the deadline,” says Brian Phillips, the spokesman for conservative Sen. Mike Lee of Utah, of the House GOP leadership plan. “You’ve got to do what you need to do to elevate this issue and put the Democrats on record as to whether or not they do or do not support the President’s amnesty.”

“The message is very clear right now,” he added. “You don’t decide in the second inning that the other pitcher is too good and you’re just going to go ahead and say, ‘Hey it’s a 4-3 ball game and we lost.’ You’ve got to play out the game.”

Senate Democratic leaders, including Appropriations Chairwoman Barbara Mikulski, have indicated they would support the House GOP leaders’ plan. When Senate Majority Leader Harry Reid called Boehner’s proposal a “big accomplishment” on Tuesday, some conservatives thought the deal was cooked.

“That made me feel like the deal was already done,” said Kansas Republican Rep. Tim Huelskamp. “That they negotiated this awhile back.”

“If Reid likes it I don’t—by definition,” he added.

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