WASHINGTON, Nov. 18 — Karl Rove, the top White House political strategist, is coming off the worst election defeat of his career to face a daunting task: saving the president’s agenda with a Congress not only controlled by Democrats, but also filled with Republican members resentful of the way he and the White House conducted the losing campaign.

White House officials say President Bush has every intention of keeping Mr. Rove on through the rest of his term. And Mr. Rove’s associates say he intends to stay, with the goal of at least salvaging Mr. Bush’s legacy and, in the process, his own.

But serious questions remain about how much influence Mr. Rove can wield and how high a profile he can assume in Washington after being so closely identified with this year’s Republican losses, not to mention six years of often brutal attacks on the same Democrats in line to control Congress for the remainder of Mr. Bush’s presidency.

Things have not gotten off to a great start since the election. Democrats are taking Mr. Rove’s continued influence at the White House — as well as some of its recent moves, like nominating conservative judges for the federal bench — as a sign that Mr. Bush’s conciliatory pledges of bipartisanship will prove to be fleeting.