Dismal new poll numbers for President Obama in Virginia and North Carolina underscore a growing danger to his 2012 re-election hopes — his job-approval ratings have dropped below 50 percent in all of the key states that he “flipped” from the Republicans in 2008.

Mr. Obama was able to win three years ago mainly because he captured nine states that had gone for Republican George W. Bush in 2004: Florida, Ohio, North Carolina, Virginia, Indiana, Colorado, Iowa, New Mexico and Nevada. Combined, those states will account for 112 electoral votes in 2012.

But with just over a year until the next election, Mr. Obama’s rating has fallen below 50 percent in every one of those states — always a warning sign for an incumbent. In only one state, Iowa, is his approval rating, 48 percent, higher than his disapproval rating, 45 percent.

“The country’s off on the wrong track, and you pay a price for that when you’re in charge,” said Glen Bolger, a partner at the Republican polling firm Public Opinion Strategies in Alexandria. “It’s all about the economy. He’s not getting the job done in the eyes of the voters.”

In Florida, where Mr. Obama took 50.9 percent of the vote in 2008, only 41 percent of those polled in a recent survey approve of the job Mr. Obama is doing; 56 percent disapprove. In Virginia, a breakthrough state for the president in 2008 when he took 52.7 percent of the vote, only 40 percent of voters now approve of him, 54 percent disapprove, and he’s trailing former Massachusetts Gov. Mitt Romney by 2 percentage points.

The website Real Clear Politics rates only one of the nine states, New Mexico, as still leaning toward Mr. Obama, with Iowa rated as a tossup. All the others are listed in the Republican camp.

Presidential spokesman Jay Carney said Mr. Obama isn’t worried about his re-election prospects.

“The president is focused on the things he needs to do as president — getting the economy going,” Mr. Carney said. “He’s not focused on his political standing or his standing in the polls.”

But since announcing his $447 billion jobs plan on Sept. 8, Mr. Obama has devoted his first three trips outside Washington to three of the “flipped” states: Virginia, North Carolina and Ohio. On Thursday, he will travel to Cincinnati, near the district of House Speaker John A. Boehner, a Republican, to highlight a crumbling bridge over the Ohio River. His jobs bill would provide tens of billions of federal dollars to fund construction projects.

Mr. Obama’s approval ratings have been hurt by sluggish growth and an unemployment rate that has remained above 9 percent nationally this year. In response, the president proposed a stimulus plan this month that is running into opposition from both parties on Capitol Hill.

The approval trends in these key states are growing worse for Mr. Obama as the weak economy persists. In Virginia, a Quinnipiac University poll released Thursday said 40 percent of voters approve of the job Mr. Obama is doing, down from 48 percent in June.

In North Carolina, the site of next year’s Democratic National Convention, 43 percent of voters approve of Mr. Obama and 53 percent disapprove. Mr. Obama won the state by 1 percentage point over Sen. John McCain, Arizona Republican, in 2008, the first time a Democrat took the Tarheel State since 1976.

“These are the purplest of the purple — the true battlegrounds for 2012,” Mr. Bolger wrote in a blog post. “One thing is certain — if the Republicans do not win at least seven of these nine states, we do not win back the White House.”

Hispanics are a key voting bloc in many of these swing states. They accounted for 9 percent of the voters in those nine states in 2008, and they favored Mr. Obama by 26 points, 62 percent to 36 percent.

In three states — Florida, New Mexico and Nevada — Hispanics were especially crucial to Mr. Obama’s victory. In Nevada, Hispanics favored Mr. Obama by 76 percent to 22 percent.

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