“He’s not the Prime Minister Tony Blair of Iraq,” General Petraeus said of Mr. Maliki on Thursday. “He does not have a parliamentary majority. He does not have his ministers in all of the different ministries,” and they “sometimes sound a bit discordant in their statements to the press and their statements to other countries. It’s a very, very challenging situation in which to lead.”

Mr. Bush was careful when he announced his new strategy in January to avoid public estimates of how quickly Mr. Maliki might take steps toward political reconciliation. Even now, White House officials are being careful not to describe with any precision the mix of benchmarks they expect Mr. Maliki to deliver.

By the time Ambassador Crocker and General Petraeus complete a comprehensive assessment of progress in September, three months after the troop increase has been fully in place, American officials are hoping that some of the pieces of crucial legislation will have passed.

But Defense Secretary Robert M. Gates found himself pressing Mr. Maliki last week to keep Parliament from taking a two-month summer break. If lawmakers remain in Baghdad, said one senior American official who did not want to be identified because he was discussing internal White House deliberations, “we’ll have some outputs then.”

He added, “That’s different from having outcomes,” drawing a distinction between a sign of activity and a sign of success, which could take considerably longer.

In public, Mr. Bush has remained enthusiastic about Mr. Maliki, with whom he talks over a secure video link every few weeks. But Mr. Bush was also publicly supportive of several of Mr. Maliki’s predecessors, even though White House officials now dismiss many of them as ill-suited for the job.

In January, Mr. Bush characterized Mr. Maliki as an architect of the troop increase plan, even while telling visiting Congressional leaders that “I said to Maliki this has to work or you’re out,” according to two officials who were in the room. Pressed on why he thought the new strategy would succeed where previous efforts had failed, Mr. Bush shot back, “Because it has to.”