Florida gave Mitt Romney the big victory he desperately needed tonight to demonstrate that he can connect with voters and may be able to bridge the ideological gulf paralyzing the Republican Party.

His support cut a wide swath across various demographic groups: Tea Partiers, Hispanics, and women. And in a pretty clear sign that Newt Gingrich’s personal baggage—admitted affairs and three wives—had caught up with him, women rejected him in Florida by a large margin. Only 29 percent of women supported him.

Romney was also seen as the more electable candidate against Barack Obama by 56 percent of voters. But among those who call themselves “very conservative,” Gingrich took 43 percent of the vote.

After attacking Gingrich relentlessly for a week, Romney ignored him in his acceptance speech, and took aim at President Obama.

“It’s been 35 months of unemployment above 8 percent, and under this president, more Americans have lost jobs and more homes have been foreclosed than under any other administration in history,” Romney told a packed room of supporters.

In a reference to the extraordinarily nasty nature of the Florida campaign, Romney told supporters that “primary contests are not easy, and they’re not supposed to be.” But he dismissed concerns that the ultimate nominee will be weakened going into the fall election.

“As this primary unfolds, our opponents in the other party have been watching, and they comfort themselves with the thought that a competitive campaign will leave us divided and weak,” he said. “But I have news for them: a competitive primary does not divide us, it prepares us. And we will beat them.”

But if Romney was talking like the nominee and looking toward the general election, Gingrich was 75 miles away vowing to throw tires in his road.

“It is now clear that this will be a two-person race between the conservative leader, Newt Gingrich, and the Massachusetts moderate,” Gingrich told his supporters. He never congratulated Romney.

Even though Gingrich was hightailing it out of Florida, he was defiant in his vow to push on. On a jumbo screen at his election headquarters in Tampa was a huge sign screaming, “46 States to Go.”

Romney snared endorsements from most of the elected officials in south Florida, but he never landed the two he really wanted: former governor Jeb Bush and Sen. Marco Rubio. Still, he benefited greatly when Rubio, a Cuban-American, called a Gingrich ad about Romney “defamatory”—forcing Gingrich to pull down the ad.

Read More Daily Beast Contributors about the Florida Primary:
Michael Tomasky: It’s Over for Newt
John Avlon: This Race Is Far From Over
Michelle Goldberg: Why Liberals Should Love Newt
David Frum: Gingrich Knows It’s Over
& More