President George W. Bush understands there is growing U.S. concern over his handling of the Iraq war but will not rely on polls to determine when to withdraw troops, his spokesman said Sunday.

"The president understands how a war can wear on a nation," White House press secretary Tony Snow said. "Whatever the bleakness is, whatever the facts are on the ground, you figure out how to win. You can't do that by reading polls."

"Most people realize simply pulling out would be an absolute unmitigated disaster," Snow said.

Meanwhile, Sen. Dianne Feinstein said she and other Democrats would introduce a resolution this week calling for a phased withdrawal, noting that Bush signed a defense bill last year calling for that in 2006.

"Three years and three months into the war, with all of the losses, the insurgency, the burgeoning civil war that's taking place, an open-ended time commitment is no longer sustainable," she said.

"We want to see an end to this thing. We want to transition the mission. That isn't cutting and running," Feinstein said on CNN's "Late Edition."

Last week, U.S. lawmakers rejected a timetable for pulling U.S. forces out of Iraq. It came after a ferociously partisan debate engineered by Republican leaders to put lawmakers on record about the war in a congressional election year.

After three years of war, approval of Bush's handling of Iraq has dipped to 33 percent, a new low, and his overall job approval rating was 35 percent in a new AP-Ipsos poll. The war has brought a U.S. death toll of 2,500 and a price tag of $320 billion (euro253 billion).

But Snow, speaking on three Sunday talk shows, said Bush has confidence the new Iraqi government under Prime Minister Nouri al-Maliki will take on a greater role in the coming months to deal with unrest and sectarian violence in the region.

"The U.S. is not going to leave until the (Iraqi) government wants us to leave and when the job is done," Snow said. "As Iraqis become more able, obviously the U.S. will move back to support roles and at some point the U.S. is going to be able to withdraw."

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Democratic Sen. Joseph Biden said he believes the American people are frustrated by the Bush administration's failure to articulate a clear strategy for winning in Iraq. Benchmarks are needed to gauge progress and limit U.S. casualties, he said.

"If I had known this president would be this incompetent, I would not have given him the authority" to go to war, said Biden, the top Democrat on the Senate Foreign Relations Committee.

But Republican Sen. Lindsey Graham said Americans should be a bit more patient, citing progress including the recent death of terrorist leader Abu Musab al-Zarqawi after a U.S. airstrike in Iraq.

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"We do need to do a better job, but it takes time," said Graham, who appeared with Biden on CBS' "Face the Nation." "Zarqawi's death was a sea change. We're now making some progress. If we do shows every Sunday talking about every mistake, we're going to lose this war."