"The differences between us are dwarfed by the differences we have with the Democratic Party," he declared.
But in the Capitol's halls, as bruised and defeated Republicans discussed what had befallen them, those internal divisions seemed only to widen.
"It's pretty hard when we have a circle of 20 people who stand up every day and say, 'Can we surrender today, Mr. Speaker?'" said Rep. Tim Huelskamp (R-Kan.), referring to moderate Republicans in the House.
Rep. Charlie Dent (R-Pa.), one of those centrists, countered that he was merely a "truth teller."
"Some people have a hard time when others state the obvious," he said, noting that Republicans cannot enact major legislation without support from Democrats, who control the Senate. "We might as well accept that reality and deal with it."
The 16-day government shutdown drew to a close Wednesday night as the House prepared to approve a Senate-passed budget compromise. But even as Congress was ending the shutdown and averting the prospect of the government defaulting on its debts, the volume of political recriminations was growing.
Republicans had initiated the confrontation last month hoping to block or delay President Obama's healthcare law. Having failed in that effort and with their internal divisions vividly exposed, they spent Wednesday in a furious round of finger-pointing in both chambers.
"Everybody is frustrated. We got to put Humpty Dumpty back together again," said Rep. Fred Upton (R-Mich.).
House Speaker John A. Boehner (R-Ohio), who has been unable to unite his troops, did not appear in danger of losing his post, in part because no challenger has stepped forward to try to take the job.
But relations between the party's moderates and tea party conservatives are raw. Both sides — but particularly tea party conservatives and advocacy groups — have threatened to try to stage primary challenges to unseat incumbents.
"If anybody should be kicked out, it probably is those Republicans — and not Speaker Boehner — who are unwilling to keep the promises that they made to the American people," said Rep. Raul Labrador (R-Idaho), a leader of the House's ardent conservatives, many of them recently elected.
Many conservatives, such as Rep. Matt Salmon (R-Ariz.), a veteran of the last government shutdown who returned to Congress this year, seemed satisfied with Boehner's leadership.
"I think he personally did a phenomenal job trying to deal with very disparate feelings and emotions and ideas and opinions," he said. "While I may still have disagreements with him, he's earned my respect."
Some moderates, by contrast, said they were increasingly unhappy with the leadership's willingness to placate the party's right wing.
"I felt like I needed to give my leaders the flexibility that they were asking for," said Rep. Aaron Schock (R-Ill.), calling himself part of a silent majority in the GOP ranks. "I'm going to be less likely to give them that flexibility … if we're going to go along with some of these tactics that I don't think are going to be successful."
In the Senate, Republicans who wrested control of the budget fight from the House to reach a bipartisan compromise expressed frustration that their House colleagues had picked a fight over Obamacare that they could not win. They worried conservatives might do the same all over again.
"We've been saying from the beginning, 'What is the endgame? How does this end? How do you achieve what you are purporting to achieve on defunding Obamacare?'" Sen. Kelly Ayotte (R-N.H.) said.
"If they are saying that the defunding issue is going to come up again in three months, then they have learned nothing from this."
The animosity stirred up by the intraparty conflict over the anti-Obamacare strategy led by tea party Sen. Ted Cruz (R-Texas) broke out in the form of speeches on the Senate floor.