WASHINGTON — Fewer Americans believe the economy is getting better and a majority disapproves of how President Barack Obama is handling it, according to a new Associated Press-GfK poll.

Republican challenger Mitt Romney has exploited those concerns and moved into a virtually even position with the president.

Three months of declining job creation have left the public increasingly glum, with only 3 out of 10 adults saying the country is headed in the right direction. Five months before the election, the economy remains Obama’s top liability.

Obama has lost the narrow lead he held just a month ago among registered voters. In the new poll, 47 percent say they will vote for the president and 44 percent for Romney, a difference that is not statistically significant. The poll also shows that Romney has recovered well from a bruising Republican primary, with more of his supporters saying they are certain to vote for him now.

Still, in a measure of Romney’s own vulnerabilities, even some voters who say they support Romney believe the president will still be re-elected. Of all adults polled, 56 percent believe Obama will win a second term.

With his Republican nomination now ensured, Romney has succeeded in unifying the party behind him and in maintaining a singular focus on making the election a referendum on Obama’s handling of the economy. The poll is not good news for the president, and it reflects fluctuations in the economy, which has shown both strength and weakness since it began to recover from the recent recession. The new survey illustrates how an ideologically divided country and a stumbling recovery have driven the two men into a tight match.

About half — 49 percent — approve of how Obama is handling his job as president, dropping him below the 50 percent mark he was above in May. Disapproval of Obama is highest — 55 percent — for his handling of the economy. Still, registered voters are split virtually evenly on whether Romney or Obama would do a better job improving it.

“I’m not going to vote for Obama,” said Raymond Back, a 60-year-old manufacturing plant manager from North Olmsted, Ohio, one of the most competitive states in this election. “It’s just the wrong thing to go. I don’t know what Romney is going to do, but this isn’t the right way.”

Obama’s overall 49 percent approval rating is not unlike the approval ratings George W. Bush faced in June 2004 during his re-election campaign, when he and his Democratic challenger, John Kerry, were also locked in a dead heat.

The polling numbers come as no surprise to either camp. Both Romney and Obama advisers have anticipated a close contest that will be driven largely by economic conditions. The Obama camp is busy trying to define Romney, hoping it is reaching more independents like Doss Comer, 58, of Jacksonville, N.C., who said he would vote for Obama again, despite the lagging economy.

“I think we are on the wrong track,” he said. “We’re not getting anywhere. We’re not growing. The unemployment rate just spiked up again.” But, he added: “I don’t trust Romney because of what he’s doing. He’s telling his business experience, that he was an investor in business. … I don’t think he has the right background any more than Obama.”

Besides weak job growth and still high unemployment, Obama is at the mercy of European countries struggling with a debt crisis that has already sent ripples across the Atlantic. At the same time, there are signs that the housing industry may be on the mend. U.S. builders started work on more single-family homes in May and requested the most permits to build homes and apartments in 3 1/2 years.

Those types of crosscurrents are also evident in politics. While preferences for November are evenly split, a majority believes Obama will still be re-elected, a shift from an even split on the question seven months ago. In December, 21 percent of Republicans said they thought Obama would win re-election; that’s risen to 31 percent now. And among independents, the share saying Obama will win has climbed from 49 percent to 60 percent. Among Democrats, it was 75 percent in both polls.

Tim Baierlein of Brandon, Fla., believes Romney would be a reassuring voice for a business community worried about regulations and higher taxes. But he said he still thinks Obama will win because the right wing of the Republican Party could alienate voters away from Romney and because, in his view, Romney lacks a clear message.

“He just comes across as very elitist and I think that’s going to hurt,” he said.

About 4 out of 10 adults say they are worse off now than they were four years ago, compared with nearly 3 out of 10 who say they are doing better now. Among those who say they’re doing worse, 60 percent say they plan to vote for Romney in November.

Amy Thackeray, 35, of Alpine, Utah, said her husband and five children experienced the economic downturn when it affected her husband’s job. “We’ve dealt with a pay cut,” she said. “We are grateful we still have a job. We live within our means. We save and we feel that in situations like this, it makes us save even more.”

“We need someone with more financial and business experience than what Obama has,” she said. “We need a president who takes one term and makes the hard decisions to put us back on the right track, and I hope it will be Romney.”

The Associated Press-GfK Poll was conducted June 14-18 by GfK Roper Public Affairs & Corporate Communications. It involved landline and cellphone interviews with 1,007 adults nationwide, including 878 registered voters. Results from the full sample have a margin of sampling error of plus or minus 4 percentage points; it is 4.2 points for registered voters.