TAMPA, Fla. – Mitt Romney routed Newt Gingrich in the Florida primary Tuesday night, rebounding smartly from an earlier defeat and taking a major step toward the Republican presidential nomination. Despite the one-sided setback, the former House speaker vowed to press on.

Romney, talking unity like a nominee, said he was ready “to lead this party and our nation” – and turn Democratic President Obama out of office. In remarks to cheering supporters, the former Massachusetts governor unleashed a strong attack on Obama and said the competitive fight for the GOP nomination “does not divide us, it prepares us” for the fall.

“Mr. President, you were elected to lead, you chose to follow, and now it’s time to get out of the way,” he declared.

Returns from 79 percent of Florida’s precincts showed Romney with 47 percent of the vote, to 32 percent for Gingrich.

Former Pennsylvania Sen. Rick Santorum had 13 percent, and Texas Rep. Ron Paul 7 percent. Neither mounted a substantial effort in the state.

The winner-take-all primary was worth 50 Republican National Convention delegates, by far the most of any primary state so far.

But the bigger prize was political momentum in the race to pick an opponent for Obama in a nation struggling to recover from the deepest recession in decades.

That belonged to Romney when he captured the New Hampshire primary three weeks ago, then swung stunningly to Gingrich when he countered with a South Carolina upset 11 days later.

Now it was back with the former Massachusetts governor, after a 10-day comeback that marked a change to more aggressive tactics, coupled with an efficient use of an overwhelming financial advantage to batter Gingrich in television commercials over a 10-day campaign.

For the first time in the campaign, exit polls showed a gender gap in Romney’s favor. He ran far better among women than Gingrich, winning just over half of their votes, to three in 10 for his rival.

About half of the women voters said they had a favorable view of Gingrich as a person, while about eight in 10 had a positive opinion of Romney.

As in Iowa, New Hampshire and South Carolina, about half of Florida primary voters said the most important factor for them was backing a candidate who can defeat Obama in November, according to early exit poll results conducted for The Associated Press and the television networks.

Not surprisingly, in a state with an unemployment rate hovering around 10 percent, about two-thirds of voters said the economy was their top issue. More than eight in 10 said they were falling behind or just keeping up.

Gingrich, combative as usual, said the race for the nomination won’t be decided until summer, “unless Romney drops out.”