Mitt Romney supporters taunted Barack Obama with chants of "four more weeks" as their candidate surged into the lead in US opinion polls, propelled by his debate win last week.

With both candidates campaigning in perennial kingmaker state Ohio, top Obama aides put a brave face on the president's slide, insisting they had always known his re-election bid would be tough.

A flurry of new polls out Tuesday showed the delayed impact of Romney's debate triumph last week in Denver.

For the first time since he accepted the Republican Party nomination, Romney topped the widely-read poll of polls conducted by the RealClearPolitics website, albeit by only 0.7 points.

He led Obama by two points in daily tracking polls by Gallup and Investors Business Daily, but the pair were tied in another tracking poll, by Rasmussen.

"Today, there are 28 days before the election," Romney told a crowd of about 12,000 people in Cuyahoga Falls, his largest rally to date in Ohio.

"I think the right chant ought to be for them: 'Four more weeks! Four more weeks!'" he added, in a play on the "Four more years" chant reserved for incumbents.

The raucous supporters obliged, and Romney followed up by letting them know just how important the first debate was.

"I actually think the people have heard what he had to say," Romney said of Obama, "and it's time for them to see him leave the White House and to say goodbye to him on November 6."

Romney's rise in the polls in part reflected his tack toward the political center during the debate, a shift he continued on Tuesday by telling an Iowa newspaper he had no plans to introduce legislation restricting abortion.

Romney did say, however, that he would restore a law ended by Obama that prohibits non-profit groups receiving federal government funds from providing abortions in other countries.

Meanwhile at an Obama rally in Columbus, Ohio, the large crowd chanted "Four more years! Four more years!" after the president took the stage.

"I need you ready to go to vote because we've got some work to do. We've got an election to win," Obama said.

"Everything that we fought for in 2008 is on the line in 2012."

Despite the clear bounce in Romney support, national polls are only one reflection of the race, and the campaigns are more interested in the eight or so swing states that will decide the election.

Obama is up in most battlegrounds, though full data is yet to emerge on local races following the debate.

And in a welcome respite for the president's camp, struggling to shake off the fallout of last week's listless debate performance, a CNN/ORC poll showed Obama holding steady in Ohio, leading 51 to 47 percent among likely voters.

No Republican has ever become president without winning Ohio.

Romney's senior aide Kevin Madden told reporters the campaign was not getting carried away by the sudden spurt, despite mounting excitement among Republicans, many of whom had feared the race was slipping away.

"I think you can't put too much stock in this idea of momentum. It's a very elusive thing," he said.

Obama's camp insisted it has long predicted a tough fight, with the president running for re-election in an uncertain economic environment.

"We've always felt this race would be close," campaign spokeswoman Jen Psaki told reporters on Air Force One.

"We've always run this race like we're five points down."

As Obama addressed his rally at Ohio State University on the first day of early voting in the state, Romney was at Cuyahoga Falls outside Cleveland with New Jersey's tough-talking Governor Chris Christie.

"Alright, Ohio, you ready to get the job done?" Christie boomed.

With a political map that still favors Obama, the focus of the race is increasingly turning to Thursday's debate between Vice President Joe Biden and Romney's running mate Paul Ryan.

Romney's itinerary Tuesday was no mistake: should Obama win both Iowa and Ohio, the Republican would have to counter with victory in several states seen as solidly Democratic if he is to oust the president from the White House.

Obama has tried to reassure disappointed Democrats that he is still hungry for victory ahead of his debate rematches with Romney on October 16 and 22.

The Obama camp said it has superior organization in Ohio, with more than 1,200 local officers to identify and mobilize voters, and plans to stress Obama's backing of an auto industry bailout that Romney opposed.

When Obama reminded Ohioans of Romney's call to let the auto industry go bankrupt, the crowd booed. "Don't boo, vote," the president said.