The decision by Mr. Boehner will probably stiffen Democratic resistance to significant cuts in entitlement spending on programs like Medicare. While Democrats were rattled by Mr. Obama’s push for a deficit-reduction plan that would trade cuts in social spending for new revenues, party leaders seemed willing to entertain the idea as part of an agreement that would resolve spending disputes for years to come. But many Democrats saw agreeing to Medicare cuts as undermining their political case against the House Republican plan to turn over the program to private insurers and provide subsidies for older Americans.

As late as in his Saturday radio and Internet address, Mr. Obama was urging lawmakers to take advantage of an “extraordinarily rare opportunity” to agree on a major budget plan and he urged them to “rise to the moment, and seize this opportunity, on behalf of all Americans, and the future we hold in common.”

Mr. Boehner was not specific about what particular tax issues led to the impasse, but a Republican familiar with the negotiations said an exchange of proposals between the speaker and the White House in recent days was unable to resolve disagreements over the “core elements” of the Republican proposal on tax reform.. The Republican said differences also remained over the extent of changes in the social programs.

Democrats have made clear that they will not back a budget deal built solely on spending cuts and are demanding a “balanced approach” that extracts some new revenues from corporate American and affluent taxpayers.

In his talks with the White House, Mr. Boehner indicated willingness to consider $1 trillion in new revenue, with most of the new money to be generated through an overhaul of the tax code that would be pushed through Congress next year. Both Republicans and Democrats expressed unease that a deal cut now could guarantee that lawmakers would follow through on tax reform.

In addition, there were hints that the budget deal could be tied to the Bush-era tax cuts due to expire next year, a prospect that made House Republicans nervous since many of them had campaigned and been elected on the promise that allowing those tax cuts to run out would amount to raising taxes.

Republicans said that Mr. Boehner decided to disclose his new position Saturday night to give the White House and Congressional leaders who are to meet Sunday evening sufficient time to make adjustments in their thinking.

The narrower package negotiated by Mr. Biden in a series of meetings with House and Senate Democrats was still considered large enough to allow for a debt hike through most of 2012. It combined a series of spending cuts that both Republicans and Democrats had identified in a range of federal agencies and programs, with some new revenue generated through options such as requiring federal employees to contribute more to their pensions, cuts in agriculture subsidies and the sale of federal assets.