There are two plausible paths to a deal on the debt ceiling. One is that the two parties come to a negotiated compromise. The other is that they don’t, and the government either defaults on its debt or stops paying military salaries and Social Security benefits, and voters and investors force the government to come to a deal. One path requires concessions on both sides. The other requires catastrophe to put so much pressure on one side or the other that they break.

Republicans are betting that the Democrats don’t have the stomach for a catastrophe, and that a negotiated compromise is essentially inevitable. As such, their leverage is their credibility when threatening catastrophe. The first part of that plan was walking away from the negotiations. The second part of that plan was to have each member of the leadership make strong, unqualified statements that there will be no tax increases in the final legislation. They’ve left themselves no further room to maneuver. Boehner will tell the president that having watched his ambitious lieutenant abandon the talks, and having been forced to say what he’s said, he simply can’t cut a deal that includes both higher taxes and his political survival.

Democrats are betting that Republicans don’t have the stomach to be blamed for a catastrophe. As the Republicans have gotten increasingly hot, they’ve remained notably cool. While Mitch McConnell is saying that the administration “is acting in bad faith” and “it’s not enough for the president to step in front of a microphone every once in a while and say a few words that someone hands him to say about jobs and the economy,” White House Press Secretary Jay Carney is refusing to return fire. “We are confident that we can continue to seek common ground and that we will achieve a balanced approach to deficit reduction,” he said today. Obama is similarly insistent on sticking to kumbaya themes. “I have a larger vision for America,” he said today, “where we work together, Democrats and Republicans, to live within our means, to cut our deficit and debt, but also to invest in what our economy needs to grow.”

As the Democrats understand it, their leverage is ensuring the public blames the Republicans for the consequences of letting the debt ceiling cave in. And Republicans are playing right along. When Eric Cantor abandoned the debt talks, he said, “the vice president deserves a great deal of credit for his leadership in bringing us this far,” and admitted that Democrats had agreed to “a blueprint to move forward to trillions of spending cuts and binding mechanisms to change the way things are done around here.” Democrats, in other words, had held up their end of the bargain. It was Republicans who were refusing to negotiate a final deal. And Republicans have admitted that.

McConnell, with all the subtlety of a Bond villain, put it plainly. “The suggestion here is that this is all just some big quid pro quo exercise between the two parties,” he said. “This is dangerous, and it’s wrong.” Really? The idea of the two parties compromising on a debt deal is dangerous and wrong?

The American people don’t think so. Perhaps that’s why Obama is more popular than any major Republican, the Democratic Party is more popular than the Republican Party, and a deficit deal that includes both tax hikes and spending cuts is more popular than a deal consisting of either element on its own. That gives the Democrats their leverage. The Republican Party begins in a worse position, and is positioning itself catastrophically, for a debt disaster. And as much as Boehner doesn’t want to lose support among the Tea Party and McConnell doesn’t want to raise taxes, what they really don’t want is to lose seats in the next election.

And so we’ve reached the game of chicken that was, perhaps, inevitable from the start. Republicans are betting that Democrats will break too early for their intransigence to harm them, and Democrats are betting that Republicans can’t weather a crisis atop an unpopular policy position and a disastrous attitude toward negotiations.

Whichever party wins, the country is likely to lose. If the Republicans win, we’re going to get an unbalanced debt deal that relies too heavily on frontloaded spending cuts, forgoes tax hikes that could further reduce the deficit, and rewards a reckless and dysfunctional model of negotiating through brinksmanship. If the Democrats win, we’re likely to see some sort of crisis before we see any sort of action, and this isn’t an economy or market that can handle much more bad news. Heads, dysfunction. Tails, catastrophe.