Though Republicans prevented tax increases from being included in the debt-ceiling deal, half of those polled said the agreement should have included increased tax revenue, while 44 percent said it should have relied on cuts alone. That issue is likely to be revisited soon: Congress is preparing to appoint a special committee to recommend ways to reduce the deficit. Sixty-three percent of those polled said that they supported raising taxes on households that earn more than $250,000 a year, as Mr. Obama has sought to do — including majorities of Democrats (80 percent), independents (61 percent) and Republicans (52 percent).

The poll found that Mr. Obama was emerging from the crisis less bruised than the Republicans in Congress.

The president’s overall job approval rating remained relatively stable, with 48 percent approving of the way he handles his job as president and 47 percent disapproving — down from the bump up he received in the spring after the killing of Osama bin Laden, but in line with how he has been viewed for nearly a year. By contrast, Speaker John A. Boehner, an Ohio Republican, saw his disapproval rating shoot up 16 points since April: 57 percent of those polled now disapprove of the way he is handling his job, while only 30 percent approve.

Americans said that they trusted Mr. Obama to make the right decisions about the economy more than the Republicans in Congress, by 47 percent to 33 percent. They were evenly divided on the question of whether he showed “strong qualities of leadership” during the negotiations, with 49 percent saying he did and 48 percent saying he did not. And they were still more likely to blame President George W. Bush for the bulk of the nation’s deficit: 44 percent said that the deficit was mostly caused by the Bush administration, 15 percent said it was mostly caused by the Obama administration and 15 percent blamed Congress.

The growing fears about the economy — amid a sinking stock market and warnings that the nation risks sliding back into recession — were reflected in the nationwide telephone poll, which was conducted Tuesday and Wednesday with 960 adults and has a margin of sampling error of plus or minus three percentage points.