“I don’t think it’s a coincidence that women were so heavily involved in trying to end this stalemate,” Senator Susan Collins, Republican of Maine, told the Times at the beginning of this week, when the default clock was still running. “Although we span the ideological spectrum, we are used to working together in a collaborative way.” The Times piece described how Collins, drawing on her connections with other women Senators, with whom she often shared meals, was putting together a bipartisan way out—and, thanks to how well women play with others, it just might work. Time, similarly, had a story called “In Shutdown Washington, Women are the Only Adults Left,” which referred approvingly to how Collins “refrained from partisan blame” while other women seemed to fall over themselves to offer compromises and, in the words of Lisa Murkowski, an Alaska Republican, be “reasonable.”

This notion that the friendliness and cheerful sacrifice of women Senators broke the fever in Washington, as though they were nursemaids who stepped in to put a firm but gentle hand on a raving person’s shoulder, has become part of the narrative of the debt-ceiling crisis. It is correct in one respect: women, in both chambers of Congress, did play a crucial, definitive role. And they do seem, on average, saner than the men. But there are some obvious cracks. For one thing, Republicans never did find their way out of a “stalemate” through compromise; they were checkmated, and got nothing. For another, it misses what those women legislators accomplished, and how. Democratic Senator Patty Murray, the chair of the Senate Budget Committee, sure didn’t refrain from partisanship. After the Senate voted to not crash the world economy, she tweeted, “If any lesson comes of these last few weeks it’s that the American people will not tolerate being held hostage.” She will be the opposite to Congressman Paul Ryan, the House Budget chair, on a bipartisan committee created as part of the bill that reopened the government, and no one expects her to be yielding.

That vote was not on the Collins deal, which included things like repealing the medical-device tax in the Affordable Care Act. Collins made a tough attempt to get the G.O.P. out of the situation it had put itself in, but it is hardly the Party of people like her these days—moderate northeasterners of either gender. In the end, the consequential thing about Collins’ move, joined by Murkowsi and Kelly Ayotte, another woman Republican, wasn’t that it was collaborative or that it struck a compromise—there was no deal. But it was meaningful as a vehicle for the more traditional elements in the G.O.P. to pull away from the Tea Party. It marked a split, not a coming together. Male Republicans, in contrast, were listening a little too considerately to the unstable elements in their Party.

Politico reported that, in the last days before the default deadline, Ayotte “teed off on Sen. Mike Lee (R-Utah), lambasting him for what she considered a failed strategy with no way out. [Ted] Cruz arrived late, but Ayotte wanted Cruz to hear this, too. She repeated her remarks, this time directing them at Cruz, too.” Collins’ effort to get something done, was part of a rebellion, not a love fest.

Politico also noted, when it came to the demise of the Collins deal:

A day earlier, the White House and Democratic leaders put the final kibosh on the Collins plan, telling the rank-and-file to back off the talks. They could not accept the terms of Collins’ offer to extend government financing at lower levels through 2014. Patty Murray of Washington and Barbara Mikulski of Maryland, two powerful Democratic chairmen, refused to consider it.

As Marc Tracy, of The New Republic, wrote, in a comment on the Politico piece, “That sounds awesome. Not too ‘collaborative,’ though.” In other words, the women in both parties were smart about their situation. A practice in collaboration may have been something the Republican women, on the losing side, drew on; but the ones who won, the Democrats, did so with admirable partisan intransigence.

The whole trope of the coöperative woman gets unbearably mawkish. “Let me say something that they kind of joked about in this process, about the women in the Senate, but the truth is, women in the Senate is a good thing. And, and you see leadership, and we’re all just glad that they allowed us to tag along so we could see how it’s done,” Senator Mark Pryor said on the Senate floor. It was probably good of him not to repeat all the jokes. “Leadership, I must fully admit, was provided primarily by women in the Senate,” John McCain said. He added, with a half-smiling mumble, “I won’t comment further on that.” As National Journal’s Marina Koren wrote, “Women make up 20 percent of the Senate. Male senators’ recent comments on the work they do there are 100 percent awkward.” (In the House, seventy-eight out of four hundred and thirty-eight Representatives are women.) But they were at least using the right word: leadership, not collaboration.

If anything, what is intriguing is the way men in the Senate occasionally deploy the unreasonableness of women in their own negotiations. Last week, the Times, in a look at where it all went wrong for John Boehner, the Speaker of the House, quoted Harry Reid’s reaction to an offer Boehner brought him in July, which would have also cut spending through 2014: “‘I didn’t like it. I’ve got a couple of tough women to deal with,’ he said, referring to Senators Patty Murray of Washington, the chairwoman of the Budget Committee, and Barbara A. Mikulski of Maryland, chairwoman of the Appropriations Committee.” And he did.

After all, if one wants a traditionalist’s caricature of a painfully oversensitive, non-authoritarian model of collaboration, look no farther than the House Republican conference. What is the Hastert rule but the grown-up version of the sort of elementary-school classroom where you have to bring a Valentine for everyone? Boehner couldn’t control his people; Nancy Pelosi, on the other hand, maintained discipline, even in the face of the “mini-C.R.’s,” bills on things like opening war memorials, that Republicans thought would help break it. She said she would have every last Democratic vote for the final bill, and she delivered them.