WASHINGTON — The House Republican leader said yesterday that GOP support could waver if President Bush’s Iraq war policy does not succeed by the fall.

The House minority leader, Rep. John Boehner, a Republican of Ohio, said Mr. Bush’s troop increase deserves a shot and that funding should continue even if benchmarks for success are not met. A senior Democrat said it would be “ridiculous” not to condition war money upon a troop withdrawal.

“We don’t even have all of the 30,000 additional troops in Iraq yet, so we’re supporting the president. We want this plan to have a chance of succeeding,” Mr. Boehner said.

“Over the course of the next three to four months, we’ll have some idea how well the plan’s working. Early signs are indicating there is clearly some success on a number of fronts,” he said.

But he added, “By the time we get to September or October, members are going to want to know how well this is working, and if it isn’t, what’s Plan B?”

Thus far, Republicans have stood behind the president’s increasingly unpopular war policies, including the troop increase and an open-ended war commitment.

Yet Mr. Boehner’s comments were an acknowledgment of the concern expressed by some lawmakers in private that their support could further damage the party, which lost control of Congress in the November elections.

The senior Republican on the Senate Foreign Relations committee, Senator Lugar of Indiana, said Mr. Boehner is correct.

“General Petraeus will be back. He’ll make a report,” Mr. Lugar said of General David Petraeus, commander of U.S. forces in Iraq. “Some things will go well. Some things will not go so well, but we’ll still have an obligation.”

The new Democratic leadership is pushing to begin pulling troops out of Iraq. Connecticut’s Senator Dodd, a Democratic presidential candidate, said congressional Republicans increasingly seem uneasy about Mr. Bush’s policies.

“So we may disagree politically here, but remember where the American public is on this issue: They want a change. They think we’re getting less secure, far more vulnerable today, than ever before, and they want a change in this policy,” he said.

Last week, Mr. Bush vetoed a $124 billion bill to provided money for Iraq and Afghanistan operations in part because it required troops to begin returning home by October 1, saying the fixed date is unworkable.

Top White House aides are negotiating with Democratic leaders on a new war-spending bill.

“It would be ridiculous to think that we’re going to just drop this fight,” said Rep. Charles Rangel, a Democrat of New York and the chairman of the tax-writing House Ways and Means Committee. “This is not our fight. This is the American people’s fight. They asked us to send a message to the president.”

“We’ve got to shake that White House until the people of the United States are heard,” Mr. Rangel said. “Sure, we’ve got to have some restrictions on the money.”

Another Democratic presidential candidate and former senator, John Edwards of North Carolina, argued against negotiating and said lawmakers should keep sending Mr. Bush the same Iraq spending bill.

“I think that America has asked the Democratic leadership in the Congress to stand firm, and that’s exactly what I’m saying they should do,” he said.

Edwards started airing a television commercial last week urging Congress to stand up to Mr. Bush and keep sending back the vetoed bill, which sparked a quarrel with Mr. Dodd.

“With all due respect, we could have used John’s vote here in the Senate on these issues here,” Mr. Dodd said.

Messrs. Dodd and Boehner appeared on “Fox News Sunday,” while Edwards was on “This Week” on ABC. Mr. Rangel spoke on “Face the Nation” on CBS while Mr. Lugar was on “Late Edition” on CNN.