WASHINGTON – Senate Republicans sharply challenged President Bush’s top military general and ambassador in Iraq today in a blatant demonstration of misgivings within the GOP about the protracted war.

“Are we going to continue to invest blood and treasure at the same rate we’re doing now? For what?” asked Senator Hagel, Republican of Nebraska, who supports legislation setting a deadline to bring troops home.

The deep-seated doubt expressed at the hearing before the Senate Foreign Relations Committee reflected just how far Congress had come since the war began over four years ago. And Republican senators raised tough questions that rivaled those asked by Democratic presidential hopefuls on the panel.

The exchanges came just a day after the top American war commander, General David Petraeus, recommended keeping the bulk of American forces in Iraq — some 130,000 troops — deployed there through next summer.

Whereas Republicans were once deferential to the thinking of officials running the war, particularly uniformed officers, Hagel and other GOP senators on the panel said they doubted that simply giving war commanders more time would necessarily yield results.

“In my judgment, some type of success in Iraq is possible, but as policymakers, we should acknowledge that we are facing extraordinarily narrow margins for achieving our goals,” said Senator Lugar of Indiana, the top Republican on the committee.

Senator Coleman, Republican of Minnesota, said he appreciates plans to return troop levels to 130,000 — down from the 168,000 currently in Iraq — but that he wants a longer-term vision other than suggestions that General Patraeus and American Ambassador Ryan Crocker will return to Capitol Hill in mid-March to give another assessment.

“Americans want to see light at the end of the tunnel,” said Mr. Coleman.

Echoing testimony given to the House yesterday, General Petraeus and Mr. Crocker acknowledged that Iraq remains largely dysfunctional but said violence in recent months had decreased since the influx of the added 30,000 troops deployed earlier this year.

Mr. Crocker said he believed Iraq had “almost completely unraveled” in late 2006 and early 2007. The increased security, if given more time, could pave the way for political reconciliation, he said.

“I do believe that Iraq’s leaders have the will to tackle the country’s pressing problems, although it will take longer than we initially anticipated because of the environment and the gravity of the issue,” Mr. Crocker said.

The stakes are high, he added.

“An Iraq that falls into chaos or civil war will mean massive human suffering — well beyond what has already occurred within Iraq’s borders,” Mr. Crocker said.

Mr. Hagel asked General Petraeus why his rosy view of conditions on the ground in Iraq differed from independent assessments on the war, as well as the views of some outspoken noncommissioned officers.

“We’ve got too many disconnects here, general,”Mr. Hagel said.

At one point in the hearing, General Petraeus said “there are 165,000 different views on the ground” and it can change daily.

The hearing fell on the anniversary of the September 11, 2001 attacks.

“The fact of the matter is that American lives remain in jeopardy and, as I said, if every single jihadi in the world was killed tomorrow, we’d still have a major, major war on our hands,” said Senator Biden, Democrat of Delaware, chairman of the Foreign Relations Committee, and a candidate for the Democratic presidential nomination.

Republican support for the Iraq war remains on shaky ground in Congress, epitomized byMr. Lugar’s opening statement today and Mr. Hagel’s heated questioning of the general’s recommendations. But that support wasn’t lost.

Many rank-and-file Republicans — like Mr. Lugar — said they still were uneasy about the lack of political progress in Iraq. But they also remained reluctant to embrace legislation ordering troops home by next spring, increasing the likelihood that Democrats will have to soften their approach if they want to pass an anti-war proposal.

Democrats had anticipated that a larger number of Republicans by now would have turned against Bush on the war because of grim poll numbers and the upcoming 2008 elections.

Without GOP support, Democrats repeatedly have fallen short of enough votes to pass legislation ordering troop withdrawals to begin this fall and be completed by spring.

In Baghdad, the Iraqi government today welcomed General Petraeus’ testimony and said the need for American military support would decrease over time.

National Security Adviser Mouwaffak al-Rubaie, reading from a government statement, said the Iraqis believed that “in the near future” the need for American and other coalition forces “will decrease.”

Moderate lawmakers say there is plenty of room for compromise in the deeply divided Congress. Aides say bipartisan proposals are in the works and that Senate Majority Leader Senator Reid of Nevada has reached out to several GOP senators to discuss potential common ground. However, a major hurdle remaining are politically influential organizations like MoveOn.org who say Democrats shouldn’t water down the debate with more moderate legislation.

Alternative legislative proposals on Iraq include:

—Ordering troop withdrawals to begin this fall, but set the spring date of completion as a nonbinding goal.

—Limit the mission of American troops to training the Iraqi security forces, fighting terrorists and protecting American assets, but leave it up to military commanders to determine force levels.

—Demanding Mr. Bush submit a new war strategy to Congress by fall that would limit the mission of American forces and begin drawing down force levels in coming months.