Rumsfeld's resignation — and Mr. Bush's pledge to work with Democrats on issues facing the nation — came after months of the president backing Rumsfeld and insisting the war in Iraq was on track. His arguments lost steam after voters catapulted Democrats to power in Tuesday's voting, giving Democrats control of both the House and Senate next year.
Sources close to Robert Gates tell CBS News correspondent David Martin that Gates seems convinced of the need to change strategy in Iraq, to replace many of the civilian political appointees at the Pentagon and to repair relations between the Secretary of Defense and senior military commanders.
At least one senior general told Martin he can't wait. As he put it, "the guy that's been beating us up for six years is now gone."
Democrats say they hope election gains would provide momentum for more than the fall of Rumsfeld.
"As long as Rumsfeld was there, it was clear to the world there would be no change in policy, so it's a necessary precondition but not a solution," Sen. Joe Biden, D-Del., said on CBS' The Early Show.
"The American people have spoken. They want an honorable solution in Iraq. They want to bring the troops home responsibly and not leave chaos behind," said Biden, who's in line to become chair of the Senate Foreign Relations Committee.
First stop next year will be legislation calling for an undetermined number of troops to come home immediately. Though Democrats are divided over exactly what to propose, they say their effort will send a loud political signal to disgruntled U.S. voters, and to Iraqis to assume more responsibility.
"I believe a number of Republicans will want to join forces here because there's a lot of unease in the country," said Sen. Carl Levin, D-Mich., in line to head the Senate Armed Services Committee in the new Congress.
That dynamic may be on display even sooner than next year.
Sen. John Warner, R-Va., the current chairman of the Senate Armed Services Committee, already has planned an Iraq hearing for next week with top military and intelligence officials testifying.
And after Mr. Bush surprised virtually the entire capital by announcing Rumsfeld's departure on Wednesday and picking former CIA Director to replace him, Warner said he wants to hold Gates' confirmation hearings this year — sessions that could become inquiries into almost every aspect of the Iraq war.
Top Democrats expect the new Congress to confirm Gates.
"They will confirm him," Biden said. "I have known Bob Gates for a long time. His view on Iraq is very different from Rumsfeld. That's based on the people he's been hanging out with, including [former Secretary of State James] Baker and others. It's a positive step."
Democrats also are awaiting the recommendations of a bipartisan panel led by Baker and former Democratic Congressman Lee Hamilton on Iraq, expected by early January or sooner.
White House counselor Dan Bartlett told The Early Show that the president "looks forward to hearing their recommendations as well."
What Gates and the rest of the panel will recommend to the president is still secret, but advisers predict one recommendation will be to name an Iraqi general as Deputy Commander of all coalition forces — American and Iraq — in the country, Martin reports.
Aides say when the new Congress convenes in January, Democrats plan to call for troops to begin coming home from Iraq and to increase money for veterans and training special operations forces. Levin and Rep. Ike Skelton, D-Mo., the next chairman of the House Armed Services Committee, said they also will push for more money to fix damaged military equipment.