Story Highlights• House fails to override President Bush's veto of war funding bill
• Neither side seems closer to reaching a compromise on war funding bill
• President Bush says he's hopeful "we can move beyond political statements"
• Sen. McConnell sets Memorial Day deadline for new agreement
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WASHINGTON (CNN) -- The House of Representatives on Wednesday failed to override President Bush's veto of a $124 billion war spending bill that included a deadline for U.S. troops to pull out of Iraq.
The 222-203 vote was far short of the two-thirds majority needed to override the veto.
Bush expressed optimism about a possible deal with Democrats on the war funding bill, but neither side seemed closer to compromise.
"I'm confident, with good will on both sides, that we can move beyond political statements," Bush said.
After the House vote, congressional leaders met with the president in what they called a "positive" exchange.
"We made our position clear. [The president] made his position clear. Now it's time for us to try to work together to come together," Democratic House Speaker Nancy Pelosi said after the president's meeting.
Senate Minority Leader Mitch McConnell said he is setting a deadline of May 28 to reach an agreement. He said he will meet Thursday with White House Chief of Staff Josh Bolton and Senate Majority Leader Harry Reid to "see if we can't work something out that is mutually agreeable."
"I think there is a widespread recognition -- probably unanimous recognition -- that we need to get this job done," McConnell said.
Bush opposes timetable, additional spending
Bush vetoed the bill because he opposes the goal of a 2008 pullout of U.S. combat troops and objects to the addition of $24 billion in other spending -- including farm relief, money for Gulf Coast reconstruction, state health-care programs and veterans' hospitals.
In a televised address Tuesday explaining the long-threatened veto, Bush said the measure "substitutes the opinions of politicians for the judgment of our military leaders."
Sen. Carl Levin, D-Michigan, chairman of the Armed Services Committee, said Wednesday that Bush vetoed "the will of the American people" expressed in November's elections.
Democratic congressional leaders said Bush must explain how he will bring the four-year-old war to a close.
"A veto means denying our troops the resources and the strategy that they need. After more than four years of a failed policy, it's time for Iraq to take responsibility for its own future," Reid, D-Nevada, told CNN's "American Morning."
Rep. John Boehner, R-Ohio, said he would still prefer a "clean bill," as Bush had demanded, but said "I think there's a way for us to work together to try to find common ground."
And Sen. Trent Lott, R-Mississippi, said finding a solution shouldn't be "rocket science."
New bill in the works
Anticipating Bush's veto, Democrats had begun crafting a bill that would strip out the troop removal language and replace it with a series of benchmarks to measure the progress of the Iraqi government.
The benchmarks would include passing laws related to the sharing of oil revenue and national reconciliation and reducing sectarian violence -- benchmarks that Bush himself has publicly pressed the Iraqis to meet.
Republicans have expressed a willingness to put benchmarks for progress on Iraq's government, as long as there is no U.S. withdrawal time frame, Pelosi said. "Benchmarks without teeth are, what, a conversation?" Pelosi asked.
McConnell, R-Kentucky, said Tuesday that he would be open to including "properly crafted" benchmarks for Iraq's government to meet in a new bill.
"I do think there are some kinds of benchmarks that might well achieve bipartisan support and might actually even conceivably be helpful to the effort in Iraq," McConnell said. "And that's what we're going to be looking for."
The big question facing lawmakers and the White House is whether to require consequences if the benchmarks aren't met. Democrats and some Republicans support consequences, while the White House has equated any kind of binding benchmarks for political progress with the kind of deadlines it has long opposed.
A senior Republican lawmaker, working behind the scenes with senators from both parties, has suggested a possible way to bridge the gap -- calling for troops to be withdrawn if the benchmarks aren't met but allowing the president to waive that requirement if he chooses.
Wednesday's give-and-take on the House floor showed how far apart the two sides are.
"Now into the fifth year of a failed policy, this administration should get a clue," Pelosi said. "It's not working."
Rep. Jerry Lewis, R-California, replied, "You've made your point. You had your dog-and-pony show. You've posed for political holy pictures on TV. Now what is your plan to support the troops?"
Republicans insist time is running out before lack of funding begins to affect the troops. (Full story)
Bush: Funds urgently needed
Bush said the money in his spending bill is urgently needed to fund U.S. troops in Iraq and Afghanistan. Most of the money would go to Iraq, where the combat operations now cost about $2 billion a week.
But the nonpartisan Congressional Research Service has concluded that the Pentagon could wage war through July without additional funding.
"Whatever our differences, surely we can agree that our troops are worthy of this funding and that we have a responsibility to get it to them without further delay," Bush said. (Watch military brass prepare for a possible money shortage )
The veto is only the second of Bush's presidency. The first, in July 2006, killed a bill that would have expanded federal funding for embryonic stem cell research.
The latest came on the fourth anniversary of Bush's 2003 speech from the flight deck of the aircraft carrier USS Abraham Lincoln, when he declared that "major combat" in Iraq was over.
More than 3,200 Americans have been killed in Iraq since then, and the war has become widely unpopular at home. (Watch how things have changed since that speech )
Sixty-six percent of Americans in a recent CNN poll said they opposed the conflict, and 60 percent said they backed Congress in its standoff with the White House.
White House spokeswoman Dana Perino accused congressional Democrats of "a trumped-up political stunt" by sending the war funding bill to Bush's desk on the speech's anniversary.
CNN's Ted Barrett, Dana Bash and Bob Costantini contributed to this report.
U.S. soldiers secure the entrance to a hospital in a restive Baghdad neighborhood.
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