From Ohio to Florida and beyond, the presidential race is tightening up as polls show voters giving Mitt Romney a second look after last week’s debate performance.

The latest swing state poll, out of New Hampshire, showed Romney closing a 15-point deficit and pulling within 6 points of President Obama. The WMUR Granite State Poll still showed Obama in the lead, but it marked a significant gain for Romney over the course of just one week.

A rapid-fire succession of state and national polls showed a similar trend.

In a national Gallup poll released Tuesday, Romney was leading 49-47 percent among likely voters. A Reuters-Ipsos national poll showed the candidates tied.

The RealClearPolitics average of polling now shows Romney leading by less than 1 percentage point in Florida, and Obama leading by the same airtight margin in Ohio. Obama was well ahead in those states just days ago.

Further, Romney’s post-debate surge appears to have all but wiped out Obama’s once double-digit lead among women voters.