WASHINGTON — With Congress in near revolt to President Bush’s call for more than 20,000 reinforcements in Iraq, the White House is counting on their nominee to command multinational forces in Iraq to persuade wavering Republicans to give the new strategy a chance.

Lieutenant General David Petraeus is tentatively scheduled to appear before the Senate Armed Services Committee Tuesday for his confirmation hearing. Widely respected by members of both parties, the general will likely be confirmed unanimously. But for a president making a last push to win back Baghdad, the hearings present an opportunity to tamp down opposition to his surge and new approach.

“We hope the Senate will take a look at what the general has to say next week and that will give them greater confidence in the strategy the president will read out to the country,” a White House official who requested anonymity said yesterday.

The stakes over the new war strategy crystallized yesterday after one Republican and two Democratic senators introduced a nonbinding resolution opposing the president’s decision to send the 21,500 soldiers to Baghdad. The resolution urged the president to engage Iraq’s neighbors in a political compromise in Iraq and to set a deadline for withdrawal.

“It is not in the national interest of the United States to deepen its military involvement in Iraq, particularly by escalating the United States presence in Iraq,” the resolution, sponsored by Senator Hagel, a Republican presidential aspirant from Nebraska, along with the Democratic chairmen of the Senate Armed Services and Foreign Relations Committees, said. The legislation has earned support from Senator Snowe, a Republican of Maine, and Senator Clinton, a Democrat of New York, who has taken on the anti-war wing of her party until now.

For the White House, a key target for their new general’s charm offensive will be Senator Brownback, a Republican presidential aspirant from Kansas.

Mr. Brownback was one of the president’s most vocal war supporters before the 2006 November elections. On policy toward Iran and Syria, he often tacked to the president’s right, meeting regularly with Iranian opposition figures.

In the last month, he has come out in favor of Syrian and Iranian engagement and against a troop surge. Yesterday on the floor of the Senate, Mr. Brownback spoke about how he carried the original Iraq Liberation Act legislation and how he attended the first meetings of the opposition group, the Iraqi National Congress in New York and London. His tone then became one of remorse, recounting his latest trip to Baghdad.

“But during my meetings last week, I found less reason for optimism,” he said. “Sunni leaders blame everything on the Shia. Shia leaders, likewise, blame everything on the Sunnis. The Kurdish leadership pointed out that the Sunni and Shia only meet when the Kurds call the meeting.” He went on to say, “All of this suggests that at the present time, the United States cares more about a peaceful Iraq than the Iraqis do. If that is the case, it is difficult to understand why more U.S. troops would make a difference.”

For General Petraeus, winning over Mr. Brownback will rely on the military man’s stellar reputation. A former Army Ranger and author of “This Man’s Army,” Andrew Exum yesterday said he has never heard anything except for enthusiasm for the general’s abilities from his colleagues in special operations.

“Aside from General Mattis, the Marine Corps commander who distinguished himself in the invasion of Iraq as well, General Petraeus was the only division commander to successfully go from high-intensity combat of the Iraqi army to a pacification operation,” Mr. Exum, who is now a fellow at the Washington Institute for Near East Policy, said.

One of the keys to General Petraeus’s success was that he paid off potential terrorists in the area his 101st Airborne commanded in Mosul and northern Iraq. However, his strategy of using discretionary funds to pacify potentially violent elements failed when the discretionary funds ran out.

After his 2003 tour in northern Iraq, General Petraeus took over the training of the national army in May 2004 as commander of the Multinational Security Transition Command. In this period, the figures the general provided were used repeatedly in the presidential campaign by the White House to justify the strategy of linking the withdrawal of American troops to performance goals for the Iraqi military. It turned out that many of the forces the general inherited were not fit for command and infiltrated with terrorists, according to a 2005 inspector general report from the Pentagon and State Department. But the failure adequately to train an Iraqi army has not tarnished the general’s reputation. He currently commands the Combined Arms Center at Fort Leavenworth, Kan., where he wrote the military’s first new counterinsurgency manual since the Vietnam War.

In his time at Fort Leavenworth, the general got to know the state’s senator, Mr. Brownback. The two, according to Mr. Brownback, became close. On January 7, after the president announced the nomination of General Petraeus but before his recent trip to the Middle East, Mr. Brownback said, “General Petraeus is an exceptionally smart and thoughtful man who will bring an intellectual creativity to his new mission, and I know that he will do a superb job.”