Mitt Romney's selection of Paul Ryan of Wisconsin as his running mate has not altered the race against the US president, Barack Obama, despite receiving huge media attention. The campaign remains neck and neck with less than three months to go, an AP-GfK poll reveals.

Overall, 47% of registered voters said they planned to back Obama and the vice-president, Joe Biden, in November, while 46% favoured Romney and Ryan. In a June AP-GfK survey the split was 47% for the president to 44% for Romney.

At the same time, there was a far wider gap when people were asked who they thought would win. Some 58% of adults said they expected Obama to be re-elected, while just 32% said they thought he'd be voted out of office.

After just over a week on the campaign trail, Ryan had a 38% favourable rating among adults, while 34%saw him unfavourably. Among registered voters, his numbers were slightly better – 40% favourable to 34% unfavourable. Ryan remained unknown to about a quarter of voters.

Romney selected the 42-year-old conservative chairman of the house budget committee on 11 August. The AP-GfK poll was conducted between 16 and 20 August.

Romney and Ryan will be crowned as the Republican presidential and vice-presidential nominees next week at the party's national convention in Tampa, Florida. The Democrats hold their convention the following week in Charlotte, North Carolina.

The closely locked contest reflects deep partisan divisions across the country.

Among true independents, those who said they did not lean toward either party, the share of undecided voters was declining, with each candidate picking up new support at about the same pace. However, Romney maintained a small advantage with the group, with the backing of 41% of independents to Obama's 30%. Some 21% still said they supported neither candidate.

Among all voters, 23% were undecided or said they havd not yet committed to their candidate.

One independent voter, Frank Nugent, a 76-year-old retired sales manager from Pittsburg, California, said he always gave both parties a chance to win him over – but not this time.

"Considering what the opposition is like, I can do nothing else but vote for Obama," he said. Part of his dislike for the GOP ticket was due to Ryan, he said, describing Romney's running mate as "further right than the bulk of the Republican party". But while he said he will vote for Obama, Nugent said he was disappointed in the president's record.

Robert Hamrick, 39, from Cedartown, Georgia, was going the other way. Although a registered Democrat, he planned to vote for the Romney-Ryan ticket, claiming Obama had been deceptive and failed to make good on his promises on the economy, jobs and government debt.

As for Ryan, Hamrick said: "He's very smart. He knows his stuff. He knows the finance. He can take apart Obamacare with ease." Hamrick is a former nursing home manager who left his job four years ago in the hope of finding one with more security – and has been mostly unemployed ever since.

The frail economy, with the unemployment rate hovering at 8.3% more than three years after the deep recession officially ended, remained the No 1 issue. Nine in 10 called it important for them and half of voters said it was "extremely important", outpacing all other issues tested by at least 10 percentage points. Two-thirds in the poll described the economy as poor.

Registered voters gave Romney a narrow lead on whom they'd trust more to handle the economy, at 48% against 44% for Obama. They also put Romney slightly ahead on who would do more to create jobs, with 47% to Obama's 43%. Among independent voters, Romney has a big lead over the president on handling the economy – 46% to 27%.

Romney often appeals to his business background as proof that he could better manage the federal government, and the poll found that voters were more likely to trust him to handle the federal budget deficit over Obama, by a 50% to 40% margin.

But it's unlikely that Ryan's background in setting Republican budgets will boost them as an issue in the campaign. The share of adults saying the budget deficit was deeply important to them dropped from 75% in February to 69% in the latest poll.

Among those who rated the economy as the top concern was Mattise Fraser, a 52-year-old Democrat whose hometown of Charlotte is gearing up for the Democratic gathering. "We're in a crisis situation now," said Fraser, who plans to vote for Obama. "The economy is crazy. There's no jobs."

Obama held a clear edge among voters on handling social issues such as abortion, 52% to 35%, and a narrow lead on handling Medicare, 48% to 42%. Medicare has grabbed a lot of attention lately, with Ryan's proposals to partly change the programme drawing criticism from Obama and other Democrats.

Of those who said Medicare was an extremely important issue, 49% said they planned to vote for Obama and 44% for Romney.

Obama's approval rating held steady at about an even split, with 49% saying they approved of the way he was handling his job and another 49% saying they disapproved.

The president remains more positively viewed than Romney and continues to be seen as more empathetic. Some 53% of adults held a "favourable" opinion of the president, compared with 44% who viewed Romney favourably. Obama also held a commanding lead among voters as the candidate who better "understands the problems of people like you", at 51% to 36% for Romney. Some 50% saw him as a stronger leader than Romney; 41% saw Romney as stronger.

Michelle Obama remained more popular than her husband, with 64% viewing her favourably and 26% unfavourably, although that's down from 70% favourable in May. Ann Romney's favourable rating was mostly unchanged since May, with 40% viewing her favourably, 27% unfavourably and nearly a third declining to say.

Overall, 35% said the US was heading in the "right direction", up from 31% in June.

Melinda Cody, a 45-year-old undecided voter in San Diego, saw positives and negatives with both candidates – and said she would vote for the candidate who did the least bullying. "When they just run a negative campaign, it backfires," she said.

The poll involved landline and mobile phone interviews with 1,006 adults nationwide, including 885 registered voters. Results for the full sample have a margin of sampling error of plus or minus 3.9, while it's 4.1 points for registered voters.