A source tells CBS News that among the topics Mr. Bush is exploring is what would happen if he sent more troops, such as "What would their mission would be?" and "Where would they come from?" reports CBS News chief White House correspondent Jim Axelrod.
"Our objective is to help the Iraqi government deal with the extremists and the killers, and support the vast majority of Iraqis who are reasonable, who want peace," President Bush said after an Oval Office meeting Tuesday with Tariq al-Hashemi.
The president took no questions about the announcement by his aides that he would wait until the new year before laying out a new course for U.S. involvement in Iraq.
"It's not ready yet," press secretary Tony Snow had told reporters earlier.
Though it had been the president's desire to unveil what he has been calling his "new way forward" before Christmas, President Bush told his staff Tuesday that it needed to wait, Snow said.
The press secretary insisted the new timing is not a reflection of a major last-minute shift by the White House, or that Mr. Bush is grasping for answers. Instead, the president knows the general direction he is likely to take his Iraq strategy and has instructed his team to address the many the practical ramifications, such as for military tactics and regional diplomacy, Snow said.
"It's a complicated business and there are a lot of things to take into account," the spokesman added.
The timing shift comes as public dissatisfaction with the president's handling of Iraq is at an all-time high, and Democrats are about to take control of Congress because of midterm elections that turned in large part on that issue.
In areleased Monday, 75 percent of Americans disapproved of how Mr. Bush is handling Iraq, while just 21 percent approved.
"The president believes that in putting together a way forward, he will be able to address a lot of the concerns that the American public has, the most important of which is, 'What is your plan for winning?'" Snow said.
Earlier Tuesday, President Bush conferred via videoconference with senior military commanders in Iraq, outgoing Defense Secretary Donald H. Rumsfeld and his replacement Robert Gates; the chairman of the Joint Chiefs of Staff, Gen. Peter Pace; and Gen. John Abizaid, the top U.S. commander in the Middle East. Participating from Iraq was Gen. George Casey, the chief U.S. commander in Iraq. Bush and Gates also had breakfast.
President Bush told al-Hashemi that the U.S. government is committed to helping the Iraqi people.
"We want to help your government be effective," Mr. Bush said, side-by-side with the Iraqi leader in the Oval Office after their private meeting. "We want your government to live up to its words and ideals."
Al-Hashemi came into the meeting promising to tell President Bush of his dismay over the Shiite-led Iraqi government's handling of security. He accused the government of not doing enough to deal with militia attacks and said he was especially concerned about Baghdad, where Sunni-Shiite violence has flared in several neighborhoods in recent days.
Afterward, al-Hashemi said he and Mr. Bush had a frank conversation and "tackled the issues." He said he will return home knowing he has friends in Washington.
"I share his views and aspirations that there is no way but success in Iraq," al-Hashemi said of President Bush.
Two retired Army generals who met with Mr. Bush on Monday said the president was very animated, asking many questions that suggested he was open to change.
The president, however, has not changed his public tone about the stakes involved in the war, the importance of victory or his definition of success — sounding much as he did in the weeks before the November elections, in which unhappiness with Iraq was a big factor in the Republicans' loss of Congress.
The administration has rejected calls for U.S. troop withdrawals until Iraq can govern and defend itself.