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.

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.

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.