Looking to change course, Mr. Bush said he has not decided whether to order a short-term surge in U.S. troops in Iraq in hopes of gaining control of the violent and chaotic situation there.
The president spoke assince being sworn in earlier in the week as Secretary of Defense.
As part of his mission in Iraq, Gates is expected to meet with commanders who worry that a surge in troops would delay Iraqis from taking control of their own security, reports CBS News chief White House correspondent Jim Axelrod.
Of this concern, Gates told reporters, "It's clearly a consideration. I think that the commanders out here have expressed a concern about that."
Mr. Bush said he has asked his new Pentagon boss to report to him as quickly as possible on plans to enlarge the size of the Army and Marine Corps.
At his traditional year-end news conference, Mr. Bush said the United States will "ask more of our Iraqi partners" in 2007, and also he pledged to work with the new Democratic Congress.
Mr. Bush didn't wait for the first question before assessing the past 12 months: "2006 was a difficult year for our troops and the Iraqi people."
As for the coming year, the president said additional sacrifices will have to be made, but he insisted the U.S. cannot give up and won't be intimidated or run out of Iraq, CBS News White House correspondent Mark Knoller reports.
"They think they can. They think it's just a matter of time before America grows weary and leaves, abandons the people of Iraq, for example," Mr. Bush said. "And that's not going to happen."
He also said he supports a moderate coalition in Iraq, a new effort by the government to "marginalize the radical and extremists" in Iraq.
Most of the questions dealt with Iraq, but the president was also asked about the pregnancy of Mary Cheney, the openly gay daughter of Vice President Dick Cheney.
"I know Mary and I like her, and I know she is going to be a fine, loving mother," he said. Neither he nor his questioner referred to Cheney's partner.
On domestic politics, Mr. Bush said he saw an opening for compromise with the Democratic-controlled Congress that convenes on Jan. 4. He cited Social Security and immigration as two major areas in which common ground might be found. He also called for fresh efforts to reduce the United States' dependence on foreign oil.
The session with reporters came at a time when the war in Iraq and the Republicans' loss of Congress have weakened the president.
The latestfound that just 21 percent of Americans approved of Mr. Bush's handling of Iraq, down from 29 percent in November.
The president opened the question-and-answer session by conceding the obvious — things haven't gone well in Iraq, where the United States has lost more than 2,900 troops in almost four years of war, without quelling the insurgency.
"The enemies of liberty ... carried out a deliberate strategy to foment sectarian violence between Sunnis and Shia. And over the course of the year they had success," he said.
"Their success hurt our efforts to help the Iraqis rebuild their country. They set back reconciliation and kept Iraq's unity government and our coalition from establishing security and stability throughout the country."
Mr. Bush also explained a striking shift in position — his statement on Tuesday that the United States is neither winning nor losing in Iraq, contrasted with his insistence at a recent news conference that it was "absolutely winning."
He said his earlier comments were meant to say that, "I believe that we're going to win, I believe that ... My comments yesterday reflected the fact that we're not succeeding nearly as fast as I had wanted."
Mr. Bush was asked whether he was like Lyndon Johnson, who had difficulty sleeping during the difficult days of the Vietnam War.
In response, the president said it was difficult knowing that "my decisions have caused young men and women to lose their lives." And yet, he said, the United States must prevail in the global war on terror — and will.
It "is the calling of our generation," he said.
As for the so-called surge in troops, Mr. Bush said, "We're looking at all options, and one of those options of course is increasing more troops.
"But in order to so, there must be a special mission that can be accomplished with more troops and that's precisely what our commanders have said."
Sending more troops will likely mean expanding the military. Right now, the Army has 507,000 soldiers and about 180,000 Marines on active duty, CBS News reports. The administration is said to be thinking about adding 60,000 to 70,000 men and women.
But finding them may not be easy. In 2005, the Army missed its recruiting goal by nearly 7,000 people, reports CBS News national correspondent Byron Pitts. This year it exceeded its goal by 635 soldiers, but only after lowering standards for recruits.
The Baker-Hamilton Commission said a quick buildup of troops could be helpful if the military commanders on the ground thought it would be effective in arresting what it called a "grave and deteriorating" situation in Iraq.
Not for the first time in his presidency, Mr. Bush also expressed frustration that classified material continuously finds its way into print.
"Turns out you can never find the leaker," he conceded.
He said it was possible an investigation is under way into the recent leak of a memo from National Security Adviser Stephen Hadley that was critical of Iraqi Prime Minister Nouri al-Maliki.