Several officials said the leadership and Ryan had solidified rank-and-file Republicans behind a shift in strategy by emphasizing a commitment to a budget that would eliminate deficits in a decade, and the sentiment was expressed Wednesday on the House floor.
"This is why I ran for office. This is why I came to Washington, D.C.," said Rep. Tom Reed of New York, first elected in 2010 as part of a tea party-flavored wave that gave Republicans their majority.
Another Republican, Rep. Michael Fitzpatrick of Pennsylvania, answered Democratic taunts: "This is not a gimmick," he said.
Already, both sides were laying down markers for the struggle ahead.
Across the Capitol, Senate Democrats had already announced their intention to approve a budget, although they have made it clear they will insist on additional tax revenue that Republicans are sure to resist.
In his Inaugural address on Monday, Obama mentioned the deficit only once, and in passing. When it came to programs likely to bear the closest scrutiny from Republican budget cutters, he said, "We must make the hard choices to reduce the cost of health care and the size of our deficit." But he also said, "The commitments we make to each other — through Medicare and Medicaid and Social Security — these things do not sap our initiative, they strength us. They do not make us a nation of takers, they free us to take the risks that make this country great."
The congressional calendar requires the House and Senate to approve versions of a budget by early spring. Assuming that happens, the two are then reconciled, and the resulting compromise sets the framework for spending and tax legislation for the fiscal year that begins on Oct. 1.
The president's signature is not required on the budget itself, but legislation that attempts to carry it out goes to him for his approval or veto.
Republicans hope public sentiment will strengthen their hand for negotiations with the White House on those bills, although there are earlier chokepoints they hope to exploit as well. In particular, across-the-board spending cuts are to take effect beginning March 1, and it is something of an article of faith among many GOP lawmakers that the president would rather agree to an alternative that targets savings.
Also, funding for most of the government expires on March 27, giving conservatives yet another chance to try and reduce overall spending. That strategy is not without considerable risk, though. Republicans suffered grievous political damage in the mid-1990s when they engineered a pair of government shutdowns in a battle with President Bill Clinton over spending.
Supporters of the debt limit bill did not estimate the additional borrowing that would occur, but the Bipartisan Policy Center forecast about $450 billion if it is signed into law by month's end. Despite the May 18 date, the group also predicted Treasury would be able to take additional steps that would allow it to meet obligations through at least the end of July.
Associated Press writer Jim Kuhnhenn contributed to this story.