"With common-sense exceptions for seniors, veterans, and our troops, we will roll back government spending to pre-stimulus, pre-bailout levels, saving us at least $100 billion in the first year alone," the pledge says.

But then Republicans took office in January and began trying to put together a bill to fund the government through the end of the fiscal year in September. The current resolution expires March 4, and Congress must act before then to keep the government functioning.

Almost immediately, Republicans began backpedaling on the pledge. First, House Budget Committee Chairman Paul Ryan (R-Wis.) explained that, because Obama's budget request was never enacted, Congress had set spending at a much lower level for the current fiscal year. As a result, the GOP would have to cut less to hit its target. Plus, the fiscal year was nearly half over, Ryan said, so he would prorate the cuts to cover only the seven months from March to September.

After receiving guidance from the nonpartisan Congressional Budget Office, House leaders proposed reducing spending by $74 billion compared with the budget request Obama submitted last February - $58 billion from appropriations unrelated to national security and $16 billion from the Pentagon. Those targets would require actual cuts of only about $32 billion, but House Appropriations Committee Chairman Harold Rogers (R-Ky.) warned that they would be painful, nonetheless.

Conservatives led by Rep. Jim Jordan (Ohio), chairman of the Republican Study Committee, were unappeased. Its ranks swollen with enthusiastic freshmen who have never taken calls from constituents angry about the loss of a favored program, the committee threatened to oppose the package on the House floor next week unless deeper cuts were adopted.

So on Thursday, Rogers vowed to come up with an additional $26 billion in reductions. But then conservatives moved the goal posts. The cuts to the Pentagon should not count, they said. The Pledge to America involved cutting $100 billion from non-defense programs. House leaders would have to come up with an additional $16 billion.

Rep. Jeff Flake (R-Ariz.) said the defense cuts weren't real anyway. While Rogers was offering a $16 billion reduction compared with Obama's request, his spending plan would actually give the Pentagon a 2 percent increase over current spending levels.

"That's the kind of math that we've ridiculed for years, and we're accepting that now," Flake said. "That's kind of bothersome to a lot of us."

Angry GOP veterans fumed that their agenda was being hijacked by newcomers who are unschooled in the intricacies of the federal budget and whose efforts threatened to torpedo any chance at a legitimate bipartisan agreement on spending.

Rep. Tom Latham (R-Iowa), a senior Appropriations Committee member and close friend of Boehner's, said Roger's initial package was probably "enactable" in a deal with the Senate, where a large number of Democrats face reelection in 2012 from states that voted Republican last fall.

Deeper cuts are unlikely to fly, however, Latham said, raising the prospect that Congress will merely extend spending at current levels to keep federal agencies open - denying Republicans a victory on their most important campaign promise.

The tension playing out on Capitol Hill was evident Wednesday night when Ryan found himself on the defensive in a conference call with tea party activists. One caller, Tamara Colbert, who heads the California-based Pasadena Patriots, asked Ryan why the GOP had dropped its $100 billion pledge.

"What we need is for our representatives to stand up and have the guts to risk everything," said Colbert, who works closely with American Solutions, the political organization run by former House speaker Newt Gingrich (Ga.) and the sponsor of the conference call.

Ryan tried to walk Colbert through the arcane math, then caught himself. "It just took me, like, five minutes to explain that," he said. "That's what's so frustrating about this issue."

Late Thursday, Republicans met for nearly an hour and a half with GOP lawmakers, trying to find a path that would win over conservatives without alienating more moderate members, including some urban Republicans whose districts would be hit hard by the cuts. Afterward, House Majority Leader Eric Cantor (Va.) said Republicans were "uniting around the fact that we are going to bring a bill to the floor next week that cuts $100 billion," though it remained unclear whether that measure would be able to overcome conservative concerns.

Late Thursday, the Study Committee's Jordan issued a statement saying, "I applaud their efforts to keep the ball moving in the right direction."

Staff writers Amy Gardner, Paul Kane, Philip Rucker, Felicia Sonmez and Peter Wallsten contributed to this report.