WASHINGTON » What gender gap?

Less than two weeks out from Election Day, Republican Mitt Romney has erased President Barack Obama’s 16-point advantage among women, a new Associated Press-GfK poll shows. And the president, in turn, has largely eliminated Romney’s edge among men.

Those churning gender dynamics leave the presidential race still a virtual dead heat, with Romney favored by 47 percent of likely voters and Obama by 45 percent, a result within the poll’s margin of sampling error, the survey shows.

After a commanding first debate performance and a generally good month, Romney has gained ground with Americans on a number of important fronts, including their confidence in how he would handle the economy and their impressions of his ability to understand their problems.

At the same time, expectations that Obama will be re-elected have slipped: Half of voters now expect the president to win a second term, down from 55 percent a month earlier.

For all the good news for Republicans, however, what matters most in the election endgame is Romney’s standing in the handful of states whose electoral votes still are up for grabs. And polls in a number of those battleground states still appear to favor Obama.

As the election nears, Romney has been playing down social issues and trying to project a more moderate stance on matters such as abortion in an effort to court female voters. The AP-GfK poll, taken Friday through Tuesday, shows Romney pulling even with Obama among women at 47-47 after lagging by 16 points a month earlier.

But now his campaign is grappling with the fallout from a comment by a Romney-endorsed Senate candidate in Indiana, who said that when a woman becomes pregnant during a rape "that’s something God intended."

Romney, through aides, quickly distanced himself from the remark by Republican Richard Mourdock. But Obama was happy to keep the issue current, telling a crowd in Florida today: "As we saw again this week, I don’t think any politician in Washington, most of whom are male, should be making health care decisions for women," Obama said. "Women can make those decisions themselves."

A renewed focus on social issues would be an unwelcome development for Romney: Among female likely voters, 55 percent say Obama would make the right decisions on women’s issues, compared with 41 percent who think Romney would.

Romney’s pitch to women has been focused squarely on the economy, making the case that what women want most is to ensure their families and their country are on a solid financial footing. The poll shows that message appears to be taking root.

A month ago, women favored Obama over Romney on the economy 56 percent to 40 percent. Now, the split has shifted to 49 percent for Romney and 45 percent for Obama.

Similarly, Obama’s lead among women as the candidate who better understands the people’s problems has narrowed considerably, from a 58-36 Obama advantage last month to a 50-43 Obama edge now.

Monica Jensen, a 55-year-old independent from Mobile, Ala., says she voted for Obama in 2008 but will shift her vote to Romney this time, largely because of the economy.

"I’m ready for a change," she said. "I want to see the economy go in a different direction."

Ginny Lewis, a Democrat and 72-year-old retired district attorney from Princeton, Ky., says she’ll vote for Romney because "I’m tired of the Republicans blaming all the debt on Democrats, so let them take over and see what they do."

Not that she’s optimistic about how that will turn out, though. "I think things will get worse before they get better," she said.

Lindsey Hornbaker, a 25-year-old graduate student and nanny, hasn’t been swayed by Romney’s charm offensive.

Hornbaker, interviewed Wednesday in Davenport, Iowa, where she was attending an Obama rally, said Romney can tweak his tone but not what she sees as a record focused far more on top income earners and out of touch with most working families.

"I heard him go out of his way to sound so moderate during the debate," she said. "And I thought: ‘Who is this? Where did this come from?’ He may sound like he’s focused on the middle class. But where’s the record?"

Obama, meanwhile, has been working to shore up his support among men, who tend to be more Republican than women. In the 2008 election, men broke 49 percent for Obama to 48 percent for John McCain, even though Obama got 53 percent of the vote overall. The president’s job approval ratings among men have tended to fall below his ratings among women throughout his first term.

A month ago, Romney’s advantage among men was 13 percentage points. Now, it’s down to 5 points, with most of the shift toward Obama coming among unmarried men.

Obama’s election chances hinge on turning out voters like Jon Gerton, a disabled construction worker from Jonesboro, Ark. Gerton’s a staunch Obama supporter — but he didn’t vote in 2008.

"It takes longer than four years to get things to the point where things are going better," Gerton said. "Four years, it’s not very long."

There has been a gender gap in every presidential election since 1980. In 2008, women were 7 percentage points more likely than men to vote for Obama.

Overall, people are significantly more optimistic about the economy and unemployment in the coming year than they have been at any point in AP-GfK polling going back to March 2011, when the poll first started asking those questions. And likely voters are even more optimistic than other adults.

Nearly six in 10 likely voters think the economy will improve in the next year, up from 46 percent last month. And 42 percent think the number of unemployed Americans will drop in the next year, up from 32 percent in September.

Count Chrysta Walker, of Cedar Lake, Ind., among the voters who are sticking with Obama because they think he’s got the right solutions for the fragile economy.

"He’s got the middle class at heart," says the 58-year-old Walker. On the economy, she says, Obama "did as well as could be expected because he didn’t get a lot of cooperation."

David Bierwirth, who owns an autograph sales business in Las Vegas, turned out at a Romney rally in Henderson, Nev., this week to show his support for the GOP nominee. To Bierwirth, his vote for Romney is all about the economy.

"I want people back to work," he says, "because then they will buy my products."

The Associated Press-GfK poll was conducted Oct. 19-23 by GfK Roper Public Affairs & Corporate Communications. It involved landline and cellphone interviews with 1,186 adults nationwide, including 839 likely voters. Results for the full sample have a margin of sampling error of plus or minus 3.5 percentage points; for likely voters it is 4.2 points.

AP News Survey Specialist Dennis Junius and Associated Press writers Stacy A. Anderson in Washington, Thomas Beaumont in Davenport, Iowa, and Ken Ritter in Henderson, Nev., contributed to this report.