WASHINGTON -- President Bush last night vetoed a congressional deadline for pulling U.S. troops from Iraq, warning that a withdrawal date would embolden America's enemies while imposing "impossible conditions" on military commanders.

It was only the second veto of Mr. Bush's presidency, and it put him at odds with Democratic leaders who captured control of Congress last year amid public discontent with the Iraq war.

"I believe setting a deadline for withdrawal would demoralize the Iraqi people, would encourage killers across the broader Middle East, and send a signal that America will not keep its commitments," the president said. "Setting a deadline for withdrawal is setting a date for failure -- and that would be irresponsible."

Democrats had attached the timetable to a $124 billion emergency spending bill for the war, calling for a military withdrawal to begin by Oct. 1.

"If the president thinks that by vetoing this bill he will stop us from working to change the direction of this war, he is mistaken," said Senate Majority Leader Harry Reid, D-Nev.

Still, the veto leaves prominent anti-war Democrats, such as Pennsylvania's Rep. John Murtha, in a bind: How do they provide critical funds for the troops while continuing to challenge the president?

A veto override, requiring the support of two-thirds of both the House and the Senate, is nearly impossible, with most Republicans in opposition. A bill that doesn't have a withdrawal deadline likely would lose the backing of many Democrats.

Congressional leaders may settle on requiring the Iraqi government to meet a series of benchmarks in the next few months, including a program for sharing oil revenue among the country's main ethnic groups and a reduction of sectarian violence.

Regardless, negotiations will be difficult. Mr. Bush has invited Democratic leaders to meet with him at the White House today to try to end the impasse.

"We look forward to working with the president to find common ground," said House Speaker Nancy Pelosi, D-Calif. "But there is great distance right now."

Mr. Murtha, D-Johnstown, is the House's highest ranking member in charge of defense spending, and he has been at the center of his party's efforts to try to use the emergency spending bill to force a redeployment of American troops.

He said yesterday that he supports a temporary, two-month spending bill, which would force the Bush administration to return quickly to Congress for more money, allowing lawmakers to play a larger oversight role in the war. But Mr. Murtha acknowledged that other congressional leaders may be reluctant to follow that approach, with other major legislative issues, such as immigration reform, waiting on the sidelines.

"My recommendation is two months," he said. "But I'm not sure if we can work it out."

During a series of recent media interviews -- including a Sunday appearance on CBS's "Face the Nation" -- Mr. Murtha created a stir by raising the specter of an impeachment threat against Mr. Bush. He sees Congress' budgetary powers as the best way to force an end to the war, but he said his office receives scores of calls about the possibility of impeaching the president.

"It may not be realistic. But he's so uncompromising," Mr. Murtha said. "The people spoke in the election. He didn't pay any attention."

White House spokeswoman Dana Perino last week dismissed such talk from other Democrats, saying the president has served honorably.

Julian Zelizer, a Boston University specialist in congressional history, said Mr. Murtha is just playing political hardball.

"Congress members sometimes like to say what the president doesn't want to hear," he said. "The threat is there. That's how bargaining goes."

A likely compromise area could involve the setting of performance targets for the Iraqis.

"Both the president and Republicans have discussed benchmarks as a way of measuring success and progress, not tying conditions to arbitrary deadlines and funding as Democrats have done," said Brian Kennedy, a spokesman for House Minority Leader John Boehner, R-Ohio. "Republicans have rejected that approach unilaterally, and will continue to do so."

Dr. Zelizer said some anti-war Democrats may be reluctant to back the benchmark strategy, but they could also view it as a stepping stone, betting that more Republicans will break with the president if there are no signs of significant progress in Iraq in the coming months.

Democrats sent the spending bill to the White House on the fourth anniversary of Mr. Bush's landing on the USS Abraham Lincoln, where he declared an end to "major combat operations" in Iraq and stood in front of a "Mission Accomplished" banner.

Ms. Pelosi said the timing was coincidental, but it was a powerful reminder of the conflict's longevity and cost, stretching beyond American involvement in World War II and topping $421 billion, according to The Associated Press.

The president yesterday asked the American public to have patience with the "surge" strategy, a gradual buildup of more than 20,000 extra troops in Iraq that started at the beginning of the year.

"The goal of this new strategy is to help the Iraqis secure their capital, so they can make progress toward reconciliation, and build a free nation that respects the rights of its people, upholds the rule of law, and fights extremists and radicals and killers alongside the United States in this war on terror," he said.

Administration officials argue that the stronger military presence will give the country's fledgling government space to work out important political compromises among Sunni and Shiite Muslims and Kurds in northern Iraq.

But Mr. Murtha, a Vietnam War veteran, said that the strategy had already failed, pointing to U.S. losses in April, when 104 soldiers were killed.

There has been a drop in sectarian violence in Baghdad in recent months, and Sunni tribesman in the volatile Anbar province have been working with Americans to combat al-Qaida terrorists, but insurgent groups have still been able to launch major attacks, causing massive civilian casualties.

"The surge is not working," Mr. Murtha said.