September 4, 2014 3:53 PM EDT

Grover Norquist and Ralph Nader spoke at a National Press Club luncheon in Washington on Thursday in a bid to promote cross-aisle government cooperation.

Nader, a left-wing consumer advocate and five-time presidential candidate, is a champion of regulation and Norquist, who founded the conservative advocacy group Americans for Tax Reform, famously wants government to be small enough to “drown it in the bathtub.” But the odd couple argued there is a broader area of agreement between liberals and conservatives than people are led to believe.

“This is not something that might happen. This is not an interesting theory. This has already happened,” Norquist said. Areas where both sides can — and have — worked together, he said, include lowering mandatory sentencing minimums, defending civil liberties and strengthening national defense while reducing cost.

Nader produced a similar list. “You don’t engage in wars of aggression. You don’t interfere with international law and constitutional law and federal law and go all over the world building up empires. You don’t allow the Pentagon to automatically get huge budgets through Congress,” he said, also mentioning cooperation on prison reform. “That’s a very important area. And that’s where there’s a very, very solid basis here.”

Both men recognized the difficulties of reaching across the aisle in the current political climate and promoted establishing civic groups whose sole purpose would be “left-right alliance advocacy,” Nader said. “We need this kind of singular focus.”

Norquist, who once referred to bipartisanship as “date rape,” was quick to distance this cooperation from political negotiation. “Right-left coalitions are areas of principled agreement on perhaps procedure, or even goals,” he said, “not a compromise where someone walks in and gives up part of his soul in order to get something.”

So why do these two men — at opposite ideological poles, one a stalwart believer in government and the other a perennial skeptic — want to promote their similarities rather than differences?

“There’s nothing else to do in this town,” Norquist said. “As long as Obama is president and there’s a Republican House… on the mega issues… nothing moves. It’s like two sumo wrestlers for the next two years that are absolutely equally matched,” he added. “Nobody is getting knocked out of the ring… for the next two years, the next 20 years, [left-right coalitions are] an area where we can make real progress.”

“We can win on things we agree on,” Nader admitted. “It’s very simple.” But he did acknowledge an obstacle to this rosy future of cooperation: Personal distaste, which he called the “yuck factor.”

And money, that is. “I’m looking for some very rich person to start funding a number of these nonprofit civic advocacy groups,” Nader said.

More Must-Read Stories From TIME

Write to Tessa Berenson at tessa.berenson@time.com.

Read More From TIME
Related Stories
EDIT POST