“Buy time?” asked an angry Senator Chuck Hagel, the Republican from Nebraska who announced Monday he would retire from the Senate next year. “For what?”

General Petraeus, pressed first by Senator Susan M. Collins, a Maine Republican who is under tremendous pressure to abandon her lukewarm support for Mr. Bush’s war strategy, and then by Senator Hillary Rodham Clinton of New York, conceded that he would be “hard-pressed” to justify America’s presence in Iraq if there is no political progress in Iraq over the next year.

Senator John W. Warner, the Republican of Virginia who is one of the party’s leading voices on foreign policy, asked whether the current strategy in Iraq is “making America safer.” General Petraeus first retreated to an explanation that he is doing his best “to achieve our objectives in Iraq.”

But when pressed again, he said: “Sir, I don’t know, actually.”

Both the general and the ambassador, who in the past have talked expansively about the regional and global effects of the Iraq war, stayed narrowly in their lanes of expertise today and stepped around repeated questions about whether a series of tactical victories in Anbar Province or some neighborhoods of Baghdad could be transferred into a broader agreement that would end a state of civil war.

Image Senators Joseph R. Biden Jr., Christopher J. Dodd and John Kerry at the Senate Foreign Relations Committee hearing on Iraq. Credit... Stephen Crowley/The New York Times

Nor would they be drawn into any estimates of how many more years a major American troop presence would be required — or even when the oft-promised training of Iraqi troops would be complete enough to allow Americans to step into the background.

“I’m as frustrated with the situation as anybody else,” an exasperated-sounding General Petraeus said in a particularly pointed exchange with Senator Robert Menendez, the New Jersey Democrat. Briefly breaking out of the flat tone in which he has delivered his analyses of troop strength and the reliability of Sunni Arab tribes who have turned against the homegrown extremist group Al Qaeda in Mesopotamia, General Petraeus said, “This is going on three years for me, on top of a year deployment to Bosnia as well, so my family also knows something about sacrifice.”