WASHINGTON — As the Democratic-led Congress failed to override a presidential veto of a war spending bill that linked funding to a troop withdrawal, talk on Capitol Hill turned to how Democratic leaders and the White House will try to shape a compromise.

By nightfall yesterday, it became clear that despite calls from the staunchest anti-war Democrats for the party to dig in its heels, the leadership would not try to send another bill to President Bush that ties needed troop funding to a timetable for withdrawal.

A more likely scenario is that Democrats will try to forge an agreement on an emergency spending bill that includes benchmarks for the Iraqi government, which many Republicans could support. What Democrats and the White House may haggle over is whether those benchmarks are binding and what type of funding they would be tied to.

Congressional leaders from both parties met with Mr. Bush at the White House yesterday afternoon, and the rhetoric on each side appeared to soften somewhat after the summit. The president said he had dispatched his chief of staff, Joshua Bolten, the national security adviser, Stephen Hadley, and the budget director, Rob Portman, to negotiate with Congress. Their first meeting is set for this morning at the Capitol.

“I’m confident that we can reach agreement,” Mr. Bush said.

The House speaker, Rep. Nancy Pelosi, said after the meeting, “Make no mistake: Democrats are committed to ending this war.”

But in an appearance later on CNN, her top deputy in the House, Rep. Steny Hoyer, sounded more conciliatory. “We’ve indicated we want to fund the troops,” the majority leader said, focusing on measures that would ensure “responsibility and accountability” by the Iraqi government rather than a strict timeline for American withdrawal. He said the party’s goal was to pass a bill by the end of the month. “I think there’s room for optimism,” he said.

Republicans and Democrats alike are facing pressure from anti-war factions. The Democratic Senate Campaign Committee is focusing on the Iraq positions of Republicans up for re-election in 2008, while a Democratic presidential candidate, John Edwards, yesterday used his first campaign ad to pressure lawmakers in his party to send Mr. Bush the same bill “again and again” until he signs it. A former North Carolina senator who left office in 2005, Mr. Edwards has sought to gain a leg up on his rivals who are still serving, including Senators Clinton and Obama, by pressuring them to support a legislative effort widely considered to be unrealistic. It became apparent yesterday that Democratic congressional leaders had ruled out that option.

Aides to Republican lawmakers predicted yesterday that the Democrats would try to retain some “face-saving” measures in a new bill. One example given was a requirement that the Iraqi government meet certain performance goals in order to receive foreign aid. That would not have an impact on funding for American troops, which could meet resistance from Republicans and the White House, but it would keep some kind of binding benchmark.

Don Stewart, a spokesman for the Republican leader in the Senate, Mitch McConnell, said he could accept certain benchmarks “as long as it’s not a surrender date by another name.”

Jim Manley, a spokesman for the majority leader, Senator Reid, declined to comment on any specifics.

Earlier yesterday, the Democrats, as expected, fell far short of overriding Mr. Bush’s veto of the $124 billion spending bill. It passed the House, 222–203. An override would have required a two-thirds majority. The Senate did not even hold a vote. Seven Democrats opposed the override, while two Republicans supported it: Rep. Walter Jones of North Carolina and Rep. Wayne Gilchrest of Maryland.