Two alphas in the fight of their lives, President Barack Obama and Republican Mitt Romney sparred with passion and grit in a debate that previewed the closing arguments of a campaign that keeps circling back to bedrock questions about which candidate can do more to strengthen the fragile economy.

Fresh off their latest encounter and with just three weeks left in the race, the candidates fan out in all directions Wednesday to pitch their tuned-up messages directly to voters on some of the campaign’s most treasured turf: Romney in Virginia, Obama in Iowa. Vice President Joe Biden is westward bound for Colorado and Nevada; GOP running mate Paul Ryan returns to all-important Ohio.

It was a re-energized Obama who showed up for Tuesday’s town hall-style debate at Hofstra University, lifting the spirits of Democrats who felt let down by the president’s limp performance in the candidates’ first encounter two weeks ago.

But Romney knew what was coming and didn’t give an inch, pressing his case even when the arguments deteriorated into did-not, did-too rejoinders that couldn’t have done much to clarify the choice for undecided voters.

Tuesday’s debate was the third installment in what amounts to a four-week-long reality TV series for Campaign 2012. Romney was the clear victor in the series debut, Biden aggressively counterpunched in the next-up vice presidential debate, and the latest faceoff featured two competitors determined to give no quarter.

It was a pushy, interruption-filled encounter filled with charges and countercharges that the other guy wasn’t telling the truth.

The season closer is coming up quickly: a foreign policy faceoff Monday at Lynn University in Boca Raton, Fla.

Romney, brimming with confidence, distilled the essence of his campaign message early in Tuesday’s 90-minute debate and repeated it often.

“I know what it takes to get this economy going,” he said over and over. And this: “We can do better.” And this: “We don’t have to settle for what we’re going through.”

Obama, with both the benefit and the burden of a record to run on, had a more nuanced message.

“The commitments I’ve made, I’ve kept,” he said. “And those that I haven’t been able to keep, it’s not for lack of trying and we’re going to get it done in a second term.”

Obama also was relentless in dismissing the merits of Romney’s policies and rejecting his characterizations of the president’s record.

“Governor Romney doesn’t have a five-point plan,” the president argued. “He has a one-point plan. And that plan is to make sure that folks at the top play by a different set of rules.”

The candidates were in each other’s faces — sometimes literally — before an audience of 82 uncommitted voters from New York. It’s a state that’s already a sure bet for Obama, but the voters there stood as proxy for millions of Americans across the nation still settling on a candidate.

“They spent a lot of time cutting down the other person,” said 22-year-old Joe Blizzard, who watched with a crowd of 500 students at the University of Cincinnati. “As someone who is undecided, it was a little disappointing.”

Fellow student Karim Aladmi, 21, was more forgiving. “It goes without saying that the knives were out,” he said. “I thought Obama had a strong performance, but Romney made him work for it. I was actually impressed by both sides.”

With just 20 days left until the election, polls show an extremely tight race nationally.

Obama appears to have 237 of the 270 electoral votes needed for victory comfortably in hand, and Romney is confident of 191. That leaves 110 electoral votes up for grabs in nine battleground states: Florida (29), Ohio (18), North Carolina (15), Virginia (13), Wisconsin (10), Colorado (9), Iowa (6), Nevada (6) and New Hampshire (4).

While Republicans have made clear gains in recent days, the president leads in several polls of Wisconsin and Ohio. No Republican has won the White House without winning Ohio.

Obama’s high command scored the latest debate as a win for their guy — but allowed that the race remains tight as ever.

“Our view is this is going to be a close race,” said senior adviser David Plouffe. “We thought that before the last debate, we think that now. … We got 53 percent of the vote last time, we’re not going to get that again.”

Ryan spoke for the Republicans in a fundraising appeal issued not long after the debate ended.

“Mitt crushed it again at tonight’s debate,” he declared, then asked for more money to help “make Mitt Romney the next president.”

In the sprint to Election Day, every aspect of the campaign seems to be taking on a fresh sense of urgency — the ads, the fundraising, the grass-roots mobilizing, the outreach to key voting blocs, particularly women.

Both sides are pouring millions upon millions into TV ads in the battleground states, and independent groups are adding buckets more.

Ann Romney, son Tagg Romney and Romney campaign manager Matt Rhoades each emailed supporters with pre-debate appeals for contributions Tuesday, and Michelle Obama and former President Bill Clinton did likewise for Obama. The president himself quickly issued a post-debate plea to “stand by me” and chip in to give him the edge in the “neck and neck” race.

A Republican-leaning independent group supporting Romney launched a new $11.1 million ad push aimed at women, with the ads set to run for a week in most of the battleground states.

Polls have showed Obama with a wide lead over Romney among women, but some recent surveys have suggested the gap is narrowing.

Both candidates seized on a question in the debate about inequities in workplace salaries to make a broad appeal to women voters.

“I want to help women in America get good work by getting a stronger economy,” said Romney. He stressed his efforts to recruit women for top administration jobs when he was Massachusetts governor, saying the outreach produced “whole binders full of women.” The offhand phrase quickly ricocheted around cyberspace.

Obama used the question to point out Romney’s plans to end federal financing for Planned Parenthood and his opposition to provisions in the president’s health-care overhaul that ensure contraception is covered by health insurance.

The debate didn’t break a lot of new ground, although Romney signaled a shift in his stance on immigration.

The GOP nominee previously had said he would veto legislation to provide a path to legalization for young illegal immigrants brought to the United States as children. But Tuesday night, he said such young people “should have a pathway to become a permanent resident of the United States.”

As the debates unfold, early voting is already under way in many states, and the push to bank as many early ballots as possible is in overdrive.

Democrats cheered when the Supreme Court on Tuesday cleared the way for Ohio voters to cast ballots on the three days before Election Day, rejecting a request by the state’s Republican elections chief and attorney general to get involved in a rancorous battle over early voting. Obama’s campaign and Ohio Democrats had sued state officials over changes in state law that took away the three days of voting for most people.

All of the political maneuvering was little more than noise for more than 1.3 million Americans: They’ve already voted.

(AP)