Twenty Republican lawmakers crowded the Senate TV studio last week to issue a threat: Meet their demands, or they will force the United States to default.

The only way to prevent the catastrophe, these Tea Party faithful said, was for the Senate to pass, and the president to sign, their plan to permanently cap spending at levels last seen in 1966, before Medicare made the nation soft.

“We want to make very clear: This is not just the best plan on the table for addressing the debt limit — this is the only plan,” first-term Sen. Mike Lee (Utah) said, vowing that “we’re otherwise going to be blowing past the debt-limit deadline.”

“We have a solution,” said Sen. Jim DeMint (S.C.). “It’s the only one that can be passed before the August 2nd deadline.”

This is the language of gangster films: Do as we say — or the girl gets it.

Yet listening to the 20 House and Senate Republicans recite their demands, it was clear they were deadly serious. And that’s why, even though a large majority of lawmakers want to avoid default, it could still happen.

A Republican leadership aide has taken to calling them the “Default Caucus”: a universe of Republicans who would sooner see the federal government default than reach a compromise with President Obama. In the House, they may well have enough clout to block a deal.

According to negotiation “game theory,” the Default Caucus has boosted Republicans’ leverage. “Your hand is greatly strengthened if you can convince the other side that you’re crazy,” said James Miller, an economist at Smith College. It has enabled House Speaker John Boehner to tell the president: The Tea Party has locked our steering wheel and we can’t swerve — so you have to.

Reports of negotiations between Boehner and Obama suggest that the president has indeed swerved, offering Republicans $3 trillion in spending cuts in exchange for future increases in taxes. Yet even that offer, which liberals would regard as surrender, wouldn’t necessarily satisfy the Default Caucus.

Obama seems to have made the rational assumption that after the Tea Party Republicans get most of what they want, they will strike a deal. But what if they aren’t bluffing and they really won’t settle for anything less than a constitutional amendment returning us to 1966? What if they aren’t merely pretending to be crazy enough to tank the economy but actually are?

“That could be happening now, if the Democrats think the Republicans are willing to swerve but they’re really not,” Miller said. “The worst scenario is you’re a madman and you can’t convince the other person of that, because then you crash.”

This possibility cannot be dismissed. So far, the Default Caucus is disregarding the advice of the Wall Street Journal editorial board, warnings from Standard & Poor’s, the record of Ronald Reagan and even the permission of Grover Norquist, the conservative loyalty enforcer who said that ending the Bush-era tax cuts would not violate lawmakers’ anti-tax pledges.

The Default Caucus has dismissed all compromises. Obama and Boehner’s “Grand Bargain”? The “Gang of Six” proposal? Senate Republican leader Mitch McConnell’s plan? No, nay, never. Even Tom Coburn’s plan to shave deficits by $9 trillion was disparaged as a “$1 trillion tax hike.”

“You have a lot of members who don’t like the idea of a compromise,” CBS News’s Nancy Cordes pointed out to Boehner at his weekly news conference, “or who don’t even want to raise the debt ceiling. Have you told them that any deal is going to have to involve some compromise?”

“I have,” the speaker said.

“How?” Cordes asked.

Boehner ignored her and solicited a different question.

Fox News’s Chad Pergram asked the speaker if he has a “sense that some of your members are locked in and that they cannot compromise?”

“I do not believe that would be anywhere close to the majority,” Boehner replied.

No? A Pew Research Center poll last week found that 53 percent of Republicans, and 65 percent of Tea Party faithful, believe that the Aug. 2 default deadline can be ignored without major problems.

At their televised session listing their demands, the Tea Party lawmakers chuckled when CNN’s Kate Bolduan asked if they were concerned about being blamed for default.

DeMint explained that Obama “manufactured this crisis.”

It’s a problem game theorists recognize. “You’re essentially empowering minorities so you can extract more,” said Daniel Diermeier of Northwestern University’s Kellogg School of Management. “But once you do that, if they are radical and don’t want to agree, you’re stuck, and the deal falls through.”