WASHINGTON — Senator Obama, the Democrat from Illinois seeking his party’s nomination for the presidency, is giving the Iraq progress report of General David Petraeus low marks, going so far as to claim the one clear success in Iraq in recent months — the rout of Al Qaeda in Anbar — has nothing to do with the military surge the general in Washington is defending.

“I’m not sure that the success in Anbar has anything to do with the surge,” Mr. Obama said today at the first of two hearings featuring General Petraeus and Ambassador Ryan Crocker. “You yourself said it was political.”

This line was previewed last week in much harsher language by Senator Schumer, a Democrat from New York, who claimed that the Anbari sheikhs had responded to the “inability” of the American Marines to provide them security. Senator Webb, a Democrat from Virginia who is himself a combat veteran of the Vietnam War and served as President Reagan’s secretary of the Navy before switching parties, also joined the Anbar doubters. He went so far as to advise General Petraeus to not attribute the success in the province on the surge.

In some ways, the turnaround in Anbar, a sanctuary for Al Qaeda as recently as December, has been, according to General Petraeus, “the most significant change” in Iraq. In presentations to the House and Senate this week, Mr. Petraeus points out that the attack levels in October of 2006 were at 1,350 while they decreased to just over 200 in August of this year.

The reason for the success, according to Mr. Crocker and General Petraeus, is the bottom up political reconciliation between the Anbar sheikhs, who once harbored Al Qaeda, and the Iraqi Shiite-led government in Baghdad and American military.

The hearing today in some ways served as a preview of the position of the Democratic contenders for their party’s presidential nomination. Senator Biden, a Democrat from Delaware who until the end of 2006 was opposed to a precipitous withdrawal from Iraq, was particularly harsh. At the end of the hearing he said he had not heard anything that persuaded him that the military was pursuing a new strategy as opposed to new tactics in Iraq.

In his opening statement, he warned, “The American people will not support an indefinite war whose sole remaining purpose is to prevent the situation in Iraq from becoming even worse. It is time to turn the corner. … We should stop the surge and start bringing troops home.”

Senator Dodd, a Democrat from Connecticut, spoke about his experience visiting a G.I. from his home state who had lost an eye. The senator said the young man told him: “We will spend a month and a half to clear an area, and in an hour and a half things are back where they were before.”