A flurry of new polls show Mitt Romney eliminating a likability gap with President Obama, but the incumbent rebuilding an advantage with female voters.

The polls suggest Romney, who has had the momentum in the race since the first presidential debate, has completely repaired the damaged image that plagued him throughout the Republican primaries.

Yet the polls also show Obama with a sizable lead among women — who had trended toward Romney after the first debate — that could help him win a second term.

{mosads}Overall, the polls suggest Obama and Romney are engaged in a strikingly close race, with daily tracking numbers and swing-state surveys offering glimmers of hope and moments of despair for both campaigns and their most adamant supporters.

Romney’s favorability ratings were historically bad as recently as late August, when an ABC News-Washington Post poll found only 40 percent of likely voters had a favorable view of him, compared to 50 percent who viewed him unfavorably. It was far and away the largest negative margin at that point in the election for any major-party candidate since the poll first began tracking the metric in 1984.

Now Romney’s favorability ratings consistently break even with Obama or move into positive territory.

The latest ABC News-Washington Post poll shows Romney at 50 percent positive and 47 negative. Other polls show an even more impressive turnaround, including a USA Today-Gallup survey, in which Romney sits at 52 percent positive, 44 negative.

Romney leads Obama in many national polls, and has moved into the lead in the RealClearPolitics average of state polls for the battlegrounds of Florida and Colorado. He has also closed the gap in several other states, including Virginia, where is tied with Romney, and in Ohio and Iowa, where Obama retains a lead.

“For many voters, the only thing they heard about Romney between the primaries and convention was a very ugly Obama ad campaign, especially in swing states,” Pew Research associate director Michael Dimock told The Hill in an interview. “The first debate was a big factor. A lot of people came into that debate with a negative impression of him … and he not only presented himself as a competent, reasonable and smart person in his demeanor, but he represented the tone of his policies in a more moderate way.”

Romney’s gains have neutralized what was once a significant advantage for the president. While Obama’s job approval rating has at times suffered, his favorability rating has, for the most part, remained positive throughout his presidency.

Most polls now show Obama hovering near break-even, along with Romney.

While polls show voters have a better opinion now of Romney, Obama has reclaimed a sizable lead among women after Romney seemed to make inroads into one of Obama’s core constituencies.

This lead could help Obama build a firewall in the key Midwest states of Ohio, Wisconsin and Iowa, where the president is clinging to a lead.

Democrats panicked earlier this month after a Pew Research study, one of the first released in the aftermath of the first debate to show Romney overtaking Obama nationally, showed Romney pulling even with Obama among women, completely erasing his 18-percentage-point advantage in the previous Pew poll.

At the time, Dimock told The Hill that Romney had seen “an across-the-board improvement on the way women feel” about him.

But the Obama campaign has refocused its attention on women’s issues, and, with the help of some GOP missteps, the strategy seems to be working.

In the latest Washington Post-ABC News poll, Obama scored his largest margin of the cycle over Romney among women, 56 to 42. Romney had closed to within 6 points of Obama in the same poll a month earlier. The president also enjoys a 13-point advantage over Romney on “women’s issues” in that poll.

Gallup pollster Frank Newport told The Hill he doesn’t think female voters ever actually left Obama, pointing to Gallup’s likely-voter survey, which, while showing Romney with his biggest lead of the cycle this week, showed Obama maintaining an 8-point lead among women.

Dimock concurred, acknowledging that the Pew survey showing Romney’s massive gains among female voters might have been affected by the survey’s proximity to Romney’s overwhelming debate victory.

“I think that poll we did was picking up the dynamic of that moment [following the debate],” he said. “My suspicion is we’ll see a gender gap that is similar to previous elections.”