WASHINGTON — House Republican leaders were forced on Tuesday night to delay a vote scheduled on their plan to raise the nation’s debt ceiling, as conservative lawmakers expressed skepticism and Congressional budget officials said the plan did not deliver the promised savings.

The pushback on the bill was the latest chaotic twist in the fiscal fracas on Capitol Hill, as the clock ticked closer to Aug. 2, when the Obama administration has warned that the nation risks defaulting on its bills. The scramble to come up with a plan that could be put to a vote, now moved from Wednesday to Thursday, represents a test of Speaker John A. Boehner’s ability to lead his restive caucus. The expected showdown over the legislation is the culmination of months of efforts by Tea Party-allied freshmen and fellow conservatives to demand a fundamentally smaller government in exchange for raising the federal borrowing limit.

Mr. Boehner rolled out a two-stage plan on Monday that would allow the $14.3 trillion federal debt limit to rise immediately by about $1 trillion in exchange for $1.2 trillion in spending cuts. The plan tied a second increase early next year to the ability of a new bipartisan Congressional committee to produce more reductions.

The plan was met with skepticism — and in many cases outright rejection — by several conservative House members who said its savings did not go far enough. President Obama and most Congressional Democrats also have rejected the proposal, saying it is only a short-term solution and could lead to market uncertainty and instability.