President Bush sat down Wednesday with House and Senate leaders of both parties to figure out the next version of an Iraq war spending bill, just minutes after the House failed to override a veto of the legislation that had included a timetable for troop withdrawal.

"Yesterday was a day that highlighted differences," Bush said of his refusal to sign the bill. "Today is the day where we can work together to find common ground."

In a speech earlier in the day, Bush said the troop withdrawal timeline Democrats wanted would have told insurgents in Iraq to wait out the United States and signaled other countries in the Middle East that the U.S. can't keep its word. As he has in the past, Bush said even those who disagreed with starting the war should understand it would be wrong to abandon it.

Senate Majority Leader Harry Reid and House Speaker Nancy Pelosi sat stone-faced as cameras snapped them sitting in the Cabinet room on either side of the president. The White House meeting started late, apparently delayed by the failed override attempt.

Despite offering few specifics of a compromise, Reid said afterward that the tone of the meeting was positive.

"I think it was also clear that the president understands that there is a separate unit of government that he has to deal with called the Congress," Reid said. "The bill that we sent him was a bill that was representative of the will of the American people and we're going to keep that in mind as we go through these negotiations."

The 222-203 vote, far short of the two-thirds majority needed for a veto override, occurred just ahead of the meeting on new legislation to finance the war, now in its fifth year. Voting to override Bush's veto were 220 Democrats and two Republicans. Voting to sustain the veto were 196 Republicans and seven Democrats.

"The president has turned a tin ear to the wishes of the American people," Pelosi, D-Calif., said during the hour-long debate before the vote. "The president wants a blank check. The Congress will not give it to him."

Click here to see how your representative voted on the veto override

But Rep. Jerry Lewis, R-Calif., urged his colleagues to sustain the veto, saying politicians should not make military decisions.

"Now is not the time for the United States to back down in its War on Terror," Lewis said.

Negotiations for a new spending bill could prove difficult. Both parties agree it should include benchmarks for progress in Iraq, but many Democrats insist that timelines for U.S. troop withdrawals if they are unmet will provide the accountability that's been missing from the war.

"Benchmarks are important, but they have to have teeth in order to be effective," Pelosi said.

Administration officials and congressional allies argue the Iraqis shouldn't be punished using a withdrawal of financial or military support.

"I am confident that with goodwill on both sides that we can move beyond political statements and agree on a bill that gives our troops the funds and flexibility to do the job that we asked them to do," he said in a speech in Washington before The Associated General Contractors of America.

House Majority Leader Steny Hoyer said before the vote that he hopes to have a new bill passed in the House in two weeks, with a final measure sent to the president before Memorial Day. "We're not going to leave our troops in harms way ... without the resources they need," said Hoyer, D-Md.

Hoyer would not speculate on exactly what the bill might look like, but said he anticipates a minimum-wage increase will be part of it. He said the bill should fund combat through Sept. 30 as Bush has requested, casting doubt that Democratic leaders will adopt a proposal by Rep. John Murtha, D-Pa., to fund the war two or three months at a time.

As for bipartisan cooperation in Congress, neither side seemed in much of a hurry Wednesday. The situation has Democratic lawmakers in a difficult position. Because they control the House and Senate, the pressure is mainly on them to craft a bill that Bush will sign, and thus avoid accusations that they failed to finance troops in a time of war.

The party's most liberal members, especially in the House, say they will vote against money for continuing the war if there's no binding language on troop drawdowns. The bill Bush rejected would require the first U.S. combat troops to be withdrawn by Oct. 1 with a goal of a complete pullout six months later.

"I think the Democrats are in a box," Rep. Eric Cantor, R-Va., said in an interview. "We're pretty resolute on our side. We are not going to tie this funding to any type of withdrawal deadline or any type of redeployment deadline."

Some Democrats believe the GOP solidarity will crack over time, noting that polls show heavy public support for a withdrawal plan.

Numerous possible compromises are being floated on Capitol Hill, all involving some combination of benchmarks. Some would require Bush to certify monthly that the Iraqi government is fully cooperating with U.S. efforts in several areas, such as giving troops the authority to pursue extremists.

The key impasse in Congress is whether to require redeployments of U.S. troops if the benchmarks are not met.

Under one proposal being floated, unmet benchmarks would cause some U.S. troops to be removed from especially violent regions such as Baghdad. They would redeploy to places in Iraq where they presumably could fight terrorists but avoid the worst centers of Sunni-Shia conflict.

A new spending bill "has got to be tied to redeployment," said Rep. Rahm Emanuel, D-Ill., the House's fourth-ranking Democratic leader. He conceded, however, that Democrats have yet to figure out where they will find the votes.

"Our members will not accept restraints on the military," House Minority Whip Roy Blunt of Missouri said. He suggested tying benchmarks to continued U.S. nonmilitary aid to Iraq, an idea that many Democrats consider too weak.

Democrats won control of the House and Senate in elections that largely focused on Iraq. They showed impressive solidarity in passing the bill that Bush vetoed Tuesday, losing only 14 House Democrats while holding 216.

But top Democrats say they have no hope of replicating that showing once they begin making even modest concessions to Bush. That makes them dependent on Republican help.

The Associated Press contributed to this report.