WASHINGTON — When President Bush delivers his new Iraq strategy Wednesday he will be facing a tense and war-weary Congress where emerging majorities in both chambers are almost certain to oppose his call to send at least 20,000 troops to win back Baghdad.

Yesterday the new speaker of the House, Rep. Nancy Pelosi, a Democrat from California, said any new budget to pay for the troop surge would “receive the harshest scrutiny.”

Among the Democratic leaders there is consensus that America should begin to exit Iraq. Today they are only divided on whether the party should pressure such a withdrawal through the annual budgeting process, as Ms. Pelosi has hinted and as Democrats did in 1974 to force an American retreat from the Vietnam War.

Speaking on NBC’s “Meet the Press,” the chairman of the Senate Foreign Relations Committee, Joseph Biden, a Democrat of Delaware, said he was not sure it was either effective or constitutional to threaten budget cuts to a standing army. For Mr. Biden, who this week will launch a month-long series of hearings on Iraq, the power of oversight and persuasion is the best course.

Sitting next to Senator Lindsey Graham, a Republican of South Carolina, he said, “The only way this is going to change is when a majority of Lindsey’s colleagues, Republicans, go to the president. That is when they are going to listen.”

Mr. Graham, who was a leading critic of the president’s clandestine interrogation policy, is not ready to take on Mr. Bush’s war strategy. But many Republicans now are getting cold feet about sending in reinforcements. Last week, for example, Senator Warner, a Republican of Virginia and the chairman of the Senate Armed Services Committee in the last Congress, warned that any strategy Mr. Bush unveiled would need time for Congress to debate it. Senator Gordon Smith, a Republican of Oregon, has also said he would favor a withdrawal if progress is not made quickly in Iraq.

Last month, Senator Coleman, the Republican of Minnesota who led the Senate’s probe into the U.N. oil for food program, told the Minneapolis Star Tribune that he would not support a troop surge. “I think it would create more targets,” he said. “I think we would put more life at risk.”

Other Republicans wary of a troop increase include Senator Collins of Maine and Senator Hagel of Nebraska. Mr. Hagel last week said the idea of sending more troops to Iraq was akin to “Alice in Wonderland.”

For now, the Republican minority leader in the Senate, Senator McConnell of Kentucky, is favoring a troop surge. Yesterday, he said he intends to support such a plan. “I think to basically begin to withdraw before the job is finished is a mistake,” Mr. McConnell said on “Fox News Sunday.”

“If the president recommends what we seem to believe he’s going to recommend, I intend to support him.”

Also supportive of a surge are Senator McCain, a Republican of Arizona, and Senator Lieberman, an independent of Connecticut. Senator Clinton of New York tells the New Yorker magazine, out today, that “she has doubts but will withhold judgment until she sees President Bush’s actual plan.” Senator Obama of Illinois tells the New Yorker, “I don’t know any military expert who says that a modest increase in troop levels is going to make a big difference … Twenty thousand troops is not going to make a difference anymore.”

Mr. Graham yesterday was impassioned when pressed by Tim Russert whether he would withdraw his support for a troop surge in a year if progress was not made in stabilizing Iraq. He said, “He is trying to come up with a strategy for victory,” he said. “I don’t think any Republican or Democrat should do anything to say this war is lost.”

Mr. Graham was particularly critical of a letter sent to President Bush on January 5 by the Senate majority leader, Senator Reid of Nevada, and Ms. Pelosi. That letter said, “Rather than deploy additional forces to Iraq, we believe the way forward is to begin the phased redeployment of our forces in the next four to six months.”

“The biggest mistake is to listen to the Pelosi and Reid doctrine and leave without thinking about what happens when we leave,” Mr. Graham said. He then asked Mr. Biden if he would have signed that letter. The Delaware senator said he would not.

One explanation for Mr. Biden’s reluctance to go along with the letter of the congressional leaders may be 2008. When asked yesterday by Mr. Russert whether he was running for president, Mr. Biden said he was and that he would file the appropriate paperwork later this month.