As President Bush prepares for the Thanksgiving holiday and enjoys a respite from the debate about the war in Iraq that's been roiling Washington in recent weeks, a senior member of his Cabinet is predicting the start of U.S. troop withdrawal from Iraq "fairly soon."

"The president has said that as soon as Iraqi forces are ready, we want to see a reduction in our own forces, and I think those days are going to be coming fairly soon when Iraqis are going to be more and more capable of carrying out the functions to secure their own future," Secretary of State Condoleezza Rice told FOX News in an interview.

Any decision on when U.S. forces start coming home, Rice said, would be a "joint" one between Iraqi and coalition leader. She added that Bush will take his guidance from commanders in the field. U.S. commanders increased troop strength in Iraq to 160,000 in advance of unprecedented elections in October and next month.

The Washington Post reported in Wednesday's editions that the Pentagon tentatively plans to reduce the number of U.S. forces in Iraq early next year by as many as three combat brigades, down from 18 there now.

The plan is basically to draw down troop levels to about 100,000 in mid 2006 but that plan is flexible. Another plan that's been in the works for some time now deals with placing U.S. troops that move out of Iraq into Kuwait. There is one brigade in Fort Reilly, Kans., that has been put on hold and officials told FOX News they are not deploying now.

The formula by which U.S. commanders measure Iraqi security success is about one U.S. battalion to four Iraqi battalion at a Level 2; Level 2 means that the troops are capable of conducting operations with only logistical support from the coalition soldiers.

"If current trends hold, we'll be able to pull significant number out of Iraq in '06, " Joint Chiefs of Staff Chairman Gen. Peter Pace told FOX News in an exclusive interview.

The Bush administration has been under fire in Congress to set a timetable for a withdrawal. Bush has repeatedly declined to set such a timetable and has said the U.S. will stay in Iraq as long as it takes to ensure the country's stability and democracy. Iraq holds parliamentary elections Dec. 15.

Rice added that for U.S. troops to come home, Iraqis need to feel not only that security has improved but that the sovereign governments if fundamentally stable.

"We know of many cases around the world where, unfortunately, cowardly suicide bombers or cowardly terrorists can take on innocent civilians — they are, unfortunately, an easy target — but where the political stability of the country is still really not in question. And I think the Iraqis need to move to that place," she told FOX News.

Meanwhile, the president arrived in central Texas with his wife, Laura, and two daughters late Tuesday evening. He spent less than a day in Washington following his return from a weeklong tour of Asia.

Overseas, the president found his meetings with world leaders, to some extent, overshadowed by Democratic attacks on his rationale for the war and the progress of U.S. efforts to train Iraqi troops.

Now, another Democratic lawmaker has joined the fray.

Freshman Sen. Barak Obama of Illinois told the Chicago Council on Foreign Relations Tuesday that he favors a "limited draw-down" of U.S. troops from the Iraqi theater. But he gave no specific numbers and stopped short of advocating a complete withdrawal, as a few other Democrats have done.

Obama said enough U.S. troops should remain to prevent Iraq from "exploding into civil war or ethnic cleansing or a haven for terrorism."

"We need not so much a timetable as a time frame," Obama said. "We don't necessarily need a tim table in the sense precise date for U.S. troops pullout but a timeframe for a withdrawal."

The traditionally hawkish Vietnam veteran Rep. John Murtha recently called for all U.S. troops to be pulled out of Iraq. The comments by the Pennsylvania Democrat caused a firestorm of criticism from other Democrats about the administration's war policies, yet very few said they agreed that pulling all troops out now was a good idea.

FOX News' Bret Baier and James Rosen contributed to this report.