The president’s job approval rating of 51 percent among all Americans marks the first time he has surpassed a majority in the poll by The Times and CBS News since immediately after Osama bin Laden was killed, in May 2011. The number of adults who say the country is on the right track has increased to 40 percent, though 54 percent say it is on the wrong track.

The coalition that helped sweep Mr. Obama into office four years ago is at least partly intact. He holds a 12-point advantage among women, while Mr. Romney holds the upper hand among men by 8 percentage points. But independent voters, who supported Mr. Obama by eight percentage points in 2008, are now breaking for Mr. Romney by six percentage points.

The poll found that a majority of voters embrace the president’s vision of a country that emphasizes community and shared responsibility over self-reliance and individual responsibility, a distinction at the core of the debate between the Republican and Democratic tickets about the proper role of government.

But with the nation’s unemployment rate still above 8 percent, a recent spike in gas prices and another impending budget showdown in Washington, a cloud of pessimism still looms, which creates an opening for Mr. Romney among frustrated voters who are looking for a change.

Looking forward, 45 percent of likely voters say they believe the next generation of Americans will be worse off and 31 percent say it will be better. On this question, there is a sharp divide among race, with black men and women far more hopeful about the future than white men and women.

When asked who understands their needs and problems, Mr. Obama has a 20-point advantage over Mr. Romney among women, compared to an 8-point advantage among men. Since a Times/CBS News poll in early March, Mr. Romney has made significant gains with voters in finding a personal connection and showing empathy; the latest survey finds 46 percent of likely voters say he understands their challenges and 48 percent say he does not.

“We’re getting further behind,” said Gregory Sowin, 55, an independent voter from Kewaskum, Wis., who owns a bar and a construction business and is frustrated by health care and other policies of the administration. In a follow-up interview, he said, “Romney can’t do any worse than Obama has done, and I’m betting my future that he can do better.”