General Petraeus’s briefing comes in a week when war-related developments are not running in the Bush administration’s favor. Nine American soldiers were killed in Iraq on Monday and 20 others wounded. And members of the family of Pat Tillman, the professional football player and Army Ranger accidentally killed by other American soldiers in Afghanistan, appeared at an emotional House hearing today and accused the Pentagon and the administration of misrepresenting the circumstances of his death.

Even as Mr. Bush and Vice President Cheney repeated their claim that a deadline for beginning a troop withdrawal would cede Iraq to America’s enemies, it has quietly been setting targets of its own for the Iraqi government of Prime Minister Nuri Kamal al-Maliki to show progress on long-delayed political accommodations.

In a telephone interview from Baghdad, the new American ambassador to Iraq, Ryan Crocker, said both President Bush and Defense Secretary Robert M. Gates had bluntly told Mr. Maliki that a failure to show results would undermine the administration’s efforts to buy him more time.

“There is Iraqi time and American time,” Mr. Crocker said. “And American time is running away from us, while Iraqi time is running at a slower place.”

Under the legislation before Congress, the United States would establish benchmarks for the Iraqi government to meet to show progress in securing the country. If the president determines the Iraqis are complying, he would be directed to begin removing troops by Oct. 1, with a goal of having most combat forces out within six months. If the president concludes the Iraqis are not making progress on the benchmarks, the pullout would begin earlier, by July.

The House narrowly approved its version of the spending measure last month when it required a full withdrawal by fall of 2008 to mollify antiwar Democrats. Several House Democrats said they would support the latest version of the legislation even though the withdrawal date is now in the form of a goal.

“It is the best we can do under the circumstances,” said Hank Johnson Jr., a first-term Democrat from Georgia.