That didn't stop right-wing commentators from berating Republicans for giving up on spending cuts. "The Republican Establishment in Washington, DC should be burned to the ground and salt spread on the remains," RedState.com blogger Erick Erickson wrote. Columnist Charles Krauthammer called the bill "a complete surrender on everything."

Inhofe chalked up the angry punditry to "demagoguing," noting that he and others who supported the measure are regularly named some of the Senate's most conservative members.

On the House side, Inhofe said, "Most of the ones that would be categorized as tea partiers are those who got in [to office] being critical of the establishment and sincerely wanting less government, less taxes, less spending. We all feel that way, but they were a little afraid they'd be portrayed as insiders, thinking, 'The electorate back home elected me to do something the establishment is not doing.'"

The inclination for conservative House members to prove their tea party credentials is no doubt driven in part by the changing congressional map. House seats are safer than they've been in decades, meaning a number of House members will face more of a political threat in a primary than they would in a general election. Influential outside groups like Club for Growth told Republican congressmen that if they voted in favor of the "fiscal cliff" deal, the group would be more likely to support a primary challenge against them.

"One of the reasons I voted 'yes' was certainly to signal we're concerned about that," Johnson said with respect to pressure that House Republicans face from outside groups. "I was willing to support his thing -- as gross as it was, in many respects -- I was willing to support it because of the overall good... so that Republicans in the House could take the position [they wanted to] and recognize it kind of freed them to vote their conscience, one way or the other."

Johnson noted that Republicans in the Senate, where they are in the minority, had notably less leverage in the debate than House Republicans. He added that the bill was needed to "limit the damage" and prevent as many people as possible from seeing an income tax hike.

That said, he added that he shares the outrage House Republicans voiced "of this just totally dysfunctional process, the business here as usual in Washington where you wait 'til the very end, play brinksmanship, to shove a bill down everyone's throat."

"I have no problem with people who voted 'no' on this," he said. "This wasn't a fun 'yes.'"

Like Johnson, Republican leaders say now is the time to turn from the "fiscal cliff" to real spending cut negotiations.

"Now that the House and Senate have acted in a bipartisan way to prevent tax increases on 99 percent of the American people, Democrats now have the opportunity--and the responsibility--to join Republicans in a serious effort to reduce Washington's out-of-control spending," McConnell said in a statement yesterday about the upcoming debt limit talks. "That's a debate the American people want. It's the debate we'll have next. And it's a debate Republicans are ready for."