Polls indicate that President Obama still has a small lead over Mitt Romney in the state. | AP Photos Tiny N.H. could punch above weight

MANCHESTER, N.H. — As Mitt Romney gains ground in crucial states like Florida and Virginia, President Barack Obama is taking steps to shore up support in smaller battlegrounds that could prove decisive in a razor-close race.

That’s because if Romney can’t put Ohio in his column — the Buckeye State has so far proved stubbornly immune to the Republican’s gains elsewhere — he’ll need to win most of the remaining swing states to capture the presidency.


( See also: POLITICO swing-state map)

So with less than three weeks until Election Day, Obama stepped away from the supersize battlegrounds Thursday to rally supporters on a warm fall day here, a state with a mere four electoral votes for the taking. New Hampshire hasn’t seenObama or Romney for well more than a month — but suddenly seems as though it may punch above its weight in this election.

The president is essentially adding mortar to his firewall. “We think we have a lead in New Hampshire,” said David Plouffe, one of Obama’s top strategists.

Plouffe added that he hasn’t “seen anything to suggest Gov. Romney has pulled close in Ohio.”

( Also on POLITICO: Latest polls from around the U.S.)

Therefore, Obama is moving to bolster the states where his campaign thinks he has a lead and which Romney would need without Ohio. As NBC’s First Read noted, Obama is boosting his TV buys in Iowa and Wisconsin. He was in Iowa Wednesday, and former President Bill Clinton and first lady Michelle Obama will attend separate events in Wisconsin on Friday.

“They both need us,” said Tom Rath, a veteran New Hampshire Republican, of the two candidates. “There’s this great scene with Tracy and Hepburn where he says, ‘There’s not much meat there, but what there is is choice.’ And that’s us. We could become dispositive this election.”

Republicans here were deeply depressed last month and wondering, following Romney’s “47 percent” gaffe, whether their chances were slipping away. But they’ve been galvanized by their standard-bearer’s Denver debate performance and believe the state is now effectively tied. Democrats, while conceding Romney has moved in polls here in the past two weeks, contend that they still have a Granite State advantage.

“I think the fact that the president is still up is a very good sign,” said Sen. Jeanne Shaheen (D-N.H.) in an interview here after the Obama rally.

Jim Demers, a Concord lobbyist and one of Obama’s earliest 2008 supporters, estimated the president’s advantage at “six or seven points.

“The majority have made up their minds,” Demers said. “There’s always a bloc of independent voters who hold out until the end. They tend to be quite moderate. And Romney’s positions on social issues has them concerned. I don’t think he has ever recovered with women since discussing contraception in the primary season.”

Public and private polling in New Hampshire indicate Romney has significantly closed the gap but is still narrowly behind. Republicans here and beyond believe that’s chiefly because of his deficit with women voters.

In their remarks at Thursday’s rally, both Shaheen and Obama emphasized gender issues such as contraception access and pay equity.

The president has made such appeals a staple of his stump speech, but in his Manchester speech, he homed in on the topic by attempting to link Romney with New Hampshire’s Republican Legislature. The GOP state House has drawn considerable local attention for passing a series of controversial laws, some regarding abortion rights.

“You’ve got a state Legislature up here that sometimes acts like it knows better when it comes to women’s own health care decisions,” Obama said. “My opponent has got the same approach.”

Shaheen, in the interview, called the New Hampshire legislators “a small group of extremists on the far right who have hijacked the agenda in the Legislature,” and said Democrats will continue to hammer Romney on gender-related issues.

“That’s one of the things that we’ll continue to talk about between now and the election,” she said.

Veteran Republicans here concede that in a year when the Democratic gubernatorial nominee and the Democratic challengers in the state’s two congressional districts are all women, voters’ views about the Legislature could impact the entire ticket. Both Romney and the GOP’s gubernatorial nominee, Ovide Lamontagne, oppose abortion rights.

“Democrats have done a good job characterizing Republicans in the [state] House as extreme,” said former state GOP Chairman Steve Duprey, a longtime party leader and donor. “But for doing that, this year would be a sweep for Republicans. I think we’re going to win but not like it was two years ago.”

In 2010, the GOP captured both House seats and the state House, fueling anticipation that Romney may be the first Republican since 2000 to win New Hampshire.

But Romney, who has a summer house on Lake Winnipesaukee and spent considerable time here earlier in the year, has not held a campaign event here since Sept. 7. And, more confounding to New Hampshire political veterans in both parties, the former Massachusetts governor is not airing ads on Boston television, which covers much of this state’s population base.

Romney is helped considerably by American Crossroads’ TV footprint here, but, head-to-head against the president, is being badly outspent in New Hampshire.

Republicans here, however, still very much believe they can capture the state and point to a notable spike in enthusiasm since the first debate. Rath said they ordered 30,000 lawn signs 10 days ago and are already out of them.

Another New Hampshire Republican, granted anonymity to speak candidly about Romney’s campaign, said the turnaround has been palpable.

“From the Olympics to pre-convention, it was hard since the flubs kept building and felt like [we were] walking around here with an anchor pushing for Mitt: Each day felt tougher than the day before,” said the Republican, adding that the “47 percent” gaffe prompted concern that Romney could drown the entire ticket.

Then came Denver.

“The debate talk even carried over to my kids’ hockey and football games — parents who had not talked politics … were all talking about [the] debate and breaking to Romney,” said this GOP hand.

Even longtime Democrats concede that Romney has found his way into contention again.

“They’re more energized,” said Terry Shumaker about New Hampshire Republicans. Shumaker, a Concord attorney and close friend of the Clintons, described the race three weeks out as “unstable.”

“I think it’s tight,” added Billy Shaheen, a longtime New Hampshire politico and the senator’s husband.

The key for Romney is to build a margin along the state’s southern border, which is heavy on moderate suburbanites who work in and around Boston.

Romney backers here believe he can win over such voters, who are familiar with him from his gubernatorial term and two presidential runs, if he can convince them he’s not the extremist Obama is attempting to portray him as.

“He is Judd Gregg, not Bob Smith,” is how Rath put it, contrasting two former Republican senators. Gregg, also a former governor, served in statewide office for decades and was viewed as a classic Yankee on fiscal issues but not seen as strident. Smith was more bombastic and was ultimately turned out of office in a primary.

Some Granite Staters believe the race could prove as close as 2000, when George W. Bush won by just 7,000 votes after Al Gore made a late push.

Kathy Sullivan, a former New Hampshire Democratic chairwoman, said she’s still optimistic and believes the Obama turnout operation will be crucial in a tight race.

“I always come back to fact that Obama campaign has been on the ground doing legwork for months and months and months,” Sullivan said.

Republicans here are also somewhat concerned that a court decision blocking a new law — which would require voters to get a New Hampshire driver’s license and register vehicles within 60 days of registering to vote — could make it easier for college students in the state who hail from elsewhere to go to the polls here. Democrats are making a major push on college campuses, and Bill Clinton recently visited the University of New Hampshire.

“My nightmare scenario is that the election is decided by New Hampshire and the narrow margin here is the result of those sorts of shenanigans,” Duprey said.