In the aftermath of the tumultuous debate over raising the debt ceiling, Americans give Washington a strong vote of no confidence, with barely a quarter of those surveyed recently saying the federal government can fix the nation’s economic problems and a large majority agreeing that the policymaking process is unstable and ineffective.

A new Washington Post poll underscores the damage done to President Obama and both political parties by the long standoff over the debt ceiling and the weakened economy. The results could have significant implications for both Republicans and Democrats, as record numbers of Americans now say they are interested in new congressional representation when they vote in November 2012.

With a double-dip recession now looming and the stock market buffeted by its steepest declines since the collapse in late 2008, the findings add another layer of pessimism to a gloomy summer. Just as the market has plunged in recent days, so, too, has public faith in the nation’s leaders to deal with the problems.

Anger at Washington has been growing for some time, but the latest political battle has resulted in an intensification of the discontent.

A majority of Americans surveyed said they oppose the recent debt-ceiling compromise, which calls for slicing about $2 trillion from the deficit over the next decade. The highest and strongest opposition comes from Republicans, but a majority of independents also oppose the deal, according to the poll. Democrats are evenly divided on the matter.

But that judgment only hints at the dissatisfaction aimed at political leaders in Washington, who must specify in excess of $1 trillion more in deficit reduction by later this fall or trigger across-the-board cuts in defense and non-defense spending.

Nearly three-quarters of Americans polled said they have little or no confidence in Washington to repair the economy. Confidence is down 21 percentage points from October 2010 and is less than half its 2002 levels. Roughly four in 10 have no confidence at all in the federal government when it comes to dealing with the economy, the poll indicates.

The number of people who expressed no confidence at all nearly doubled since October 2010. Almost half of independents said “none” when asked about their confidence, more than double the proportion saying so last fall.

Nearly eight in 10 of Americans polled were dissatisfied with the way the political system is working, up dramatically from late 2009. The unhappiness is intense, with 45 percent saying they are very dissatisfied. That feeling is shared widely across party lines. Independents are the most disgruntled, with 51 percent calling themselves very dissatisfied.

More than seven in 10 said Washington is focused on the “wrong things.” That too is sharply higher than it was just 10 months ago. Two-thirds of Republicans who see the government as focused on the wrong things said Obama and the Democrats are to blame, and Democrats were nearly as likely to point the finger at the GOP. Among independents, a plurality — 43 percent — volunteered that both sides are at fault.

Half the country agrees with the assessment of the nation’s financial situation rendered by Standard & Poor’s, which downgraded the U.S. credit rating for the first time in history. The poll suggests that the decision by S&P had a powerful ripple effect, with 80 percent saying they had heard about the downgrading, and 45 percent saying they had heard “a lot” about it.

The Obama administration took sharp issue last weekend with the action by Standard & Poor’s, arguing that the rating agency made a $2 trillion miscalculation. But the public widely endorses S&P’s condemnation of the state of the U.S. political system, which the rating agency said led to the decision to downgrade.

S&P described the political system as one that has become “less stable, less effective and less predictable.” Asked about the S&P assessment, 71 percent of Americans polled called it fair. On the blame front, 36 percent said the GOP is culpable for the downgrade, 31 percent blamed Obama and fellow Democrats and 22 percent blamed both sides equally.

The decline in confidence has potentially profound implications for coming elections, although the anger appears directed evenly between the two parties. Among those who said Washington is focused on the wrong issues, 30 percent blamed Obama and Democrats, 30 percent blamed Republicans and 32 percent blamed both sides equally.

Confidence in Obama to make the right decisions for the country’s economic future is down 10 points, to 33 percent, since January. Confidence in congressional Republicans, at 35 percent in January, dropped to 18 percent.

More Americans polled said both Obama and Republicans have made things worse than said either side has made progress, although Republicans were judged more harshly on this question.

Just 10 percent of those surveyed said Republicans have made progress in solving major problems, compared with 19 percent who said as much of Obama. Thirty-five percent said Republicans have made things worse, and 28 percent said the same about the president.

Obama’s overall job ratings were 44 percent approval and 46 percent disapproval in the new poll, both down from three weeks ago, when he was at 47 and 48 percent, respectively. In this one-night poll, 10 percent expressed no opinion on this question, twice the mid-July level.

There was one bright spot in the poll: 77 percent of Americans agree with this statement: “Whatever its faults, the United States still has the best system of government in the world.” That number was unmoved from October 2010.

Polling manager Peyton M. Craighill and analyst Scott Clement contributed to this report.