From one political angle, it had special appeal. By persuading Democrats to endorse Medicare cuts, the speaker could have neutralized an issue that Democrats have been bludgeoning Republicans with since the House budget this spring called for converting that government insurance program into one subsidizing older Americans in private health plans.

But his motivations to back away were evidently stronger. The deal, which required roughly $1 trillion in new revenue, represented a serious political risk for Mr. Boehner, who found himself caught between the push for a legislative achievement and the Tea Party sentiments of his new majority and ambivalence of his top lieutenants.

By all accounts, the agreement taking shape called for closing corporate tax loopholes. And it was linked to a broad tax overhaul that could have left uncertain the fate of tax breaks for the nation’s affluent, which are due to expire after 2012. That was going to cause serious trouble with Republicans who are wedded to those Bush-era tax cuts and who consider allowing them to expire equivalent to a tax hike.

Mr. Boehner and the White House were engaged in delicate talks on the timing of the tax changes and how to package the plan so that it could be seen as not raising taxes to gain new revenue. The speaker argued that the tax rewrite would produce new revenues through economic growth and an expansion of the tax base. And he was pushing a legislative trigger to make certain that the tax changes occurred.

But fellow Republicans were not on board. At the White House meeting where Mr. Boehner said he wanted to go big, Representative Eric Cantor of Virginia, the No. 2 House Republican, threw cold water on the idea, saying the negotiations should focus on a midrange deal like the $2 trillion one that Vice President Joseph R. Biden Jr. had been leading. Those earlier negotiations broke down over potential tax increases as well.

“As Eric has said for weeks, tax increases that the Democrats are insisting upon cannot pass the House and are the last thing Congress should be doing with so many people out of work,” said Brad Dayspring, a spokesman for Mr. Cantor. “Eric has always believed the Biden group identified between $2 trillion and $2.5 trillion in spending cuts that could represent the framework for an agreement.”