TAMPA, Fla. — Mitt Romney didn't just win in Florida, he won big.

But not big enough to end what has become a bitter two-man race for the GOP presidential nomination, between Romney and former U.S. House speaker Newt Gingrich.

Romney's victory

In his victory speech, Romney sought to reassure Republicans that the battle isn't going to hurt the party's chances of defeating the Democratic candidate, President Barack Obama, in November.

"A competitive primary does not divide us. It prepares us," Romney told a cheering and flag-waving crowd of supporters jammed into a Tampa convention center ballroom. "And we will win."

He made a point of congratulating his opponents on "a hard-fought campaign," but did not refer to Gingrich or the other two candidates still in the race, Texas Rep. Ron Paul and former Pennsylvania Sen. Rick Santorum

Instead, after days of going on the offensive against Gingrich in campaign speeches and in television commercials that filled the Florida airwaves, Romney pivoted in his victory speech to target Obama, offering new, harsher jabs at the president.

"Leadership is about taking responsibility, not making excuses," Romney said. "Mr. President, you were elected to lead, you chose to follow, and now it's time for you to get out the way."

A shift in strategy

But Romney isn't likely to let up on Gingrich in the upcoming races, starting with Nevada's Republican caucuses on Saturday.

He's "going to defend himself and he will continue to draw the distinctions," one of his said Rep. Jason Chaffetz, R-Utah, one of Romney's key surrogates. "If you don't answer the criticism, it runs a chance of sticking."

That's what Romney found out in South Carolina, where he'd hope to wrap up the nomination earlier this month, but ended up losing to Gingrich amid attacks on his business dealings and personal wealth.

In Florida, Romney shifted his strategy to go after the former U.S. House speaker's ties to the troubled government-backed mortgage lender Freddie Mac. Gingrich has vowed to keep the race going through the party's nominating convention in August.

Chaffetz, who will rejoin the campaign Thursday in Nevada, said Romney "was very good at showing the passion and the fight in his belly. I think people wanted to see that."

University of Utah Hinckley Institute of Politics head Kirk Jowers, a longtime Romney adviser, said Florida sends a message to voters in the upcoming primary states.

"South Carolina seemed to call in to question whether he had the fight necessary to take on Obama and his billion dollars," Jowers said. "There's no question that Florida answered Mitt is ready, willing and able."

Jowers said Romney was not "unnecessarily hostile and I don't see him changing that. But he won't let someone like Newt Gingrich ambush him again."

What voters thought

Tampa attorney Norma Reno said even though she didn't vote for Romney, he should be considered the party's nominee.

"I voted for Gingrich today because I think he's the best and the most qualified person for the position," Reno, an attorney, said. "But tomorrow, I'm going to erase that from my mind."

Reno said the in-party fighting has gone on long enough.

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Despite Gingrich, Romney says he'll get the nomination

No one expects the race for the GOP presidential nomination to be settled by the results of Tuesday's Florida primary, but Mitt Romney said it will be his name on the November ballot.

"I need to know who the candidate is, that this is the person I'm going to support all the way," she said. "No doubt about it. Many people think that way, especially Hispanics."

Still, Reno said she has concerns about Romney's ability to stand up to communist leaders, let alone the Democratic candidate, President Barack Obama.

"I don't think he has the ability to face these traitors, these communist dictators," Reno said of Cuba's Raul Castro and Venezuela's Hugo Chavez, both reviled by many Hispanics. "He's not tough enough."

Reno questioned Romney's more negative campaign in Florida. She said she has trouble with him changing his message.

"You are going to come with a different face to me? No," Reno said. "I don't think he's sincere."

Cliff Levy, a real estate developer, cast his vote for Romney at the Christ the King Catholic church in an upscale Tampa neighborhood.

"I just like him all the way around. He's a good man, a good person with good business smarts," Levy said.

He said while he was disappointed at how negative the race has been, "that's what makes our country great, too. You can do that all the way to the end."

Robert Mabry, a retired Naval officer, said he voted for Rick Santorum, one of the two remaining candidates in the race who left Florida early.

Mabry said he realizes the former Pennsylvania senator has little chance of winning, but felt the other candidates all had too many flaws.

"I think Romney needs to be perceived as somebody who can effectively defeat Obama. He can't be 'Mr. Nice Guy,' " Mabry said.

Romney's tougher talk in Florida is a start, he said. "In the past, he's been pretty lame."

Carol Mitsch was among those cheering at Romney's victory party.

"I was very disappointed last time, in '08," Mitsch said, referring to Romney's failed bid for the White House four years ago. She said she likes the new, more aggressive Romney who's emerged in Florida.

"It's not typically his style," Mitsch said. "I think his niceness put him in the losing column last time."

On to Nevada

David Damore, a political science professor at the University of Nevada, Las Vegas, said he expects Romney "to keep the boot down on Gingrich" in Nevada. "I think he wants to finish off Gingrich," Damore said.

While Romney is seen as the favorite in Nevada because of the large number of voters who share his Mormon faith, Damore said there is "a significant anti-Romney vote out there looking for a place to go."

Romney needs to be careful not to be seen as too aggressive, University of South Florida political science professor Susan MacManus said.

"That ends up biting you," she said. Romney would do well to "keep Gingrich off guard a little bit. He doesn't have to do a lot of it."

MacManus said Romney won Florida through a combination of coming across tough in debates, saturating the airwaves with commercials critical of Gingrich, and sounding like a frontrunner to the media.

That may not work elsewhere, she cautioned. "Every state is different. I think that's what we're seeing in this 'winner a week' kind of thing."

Romney has won two of the four presidential contests so far, New Hampshire and Florida. He had been declared the winner of Iowa's GOP caucus poll, but in the final tally ended up behind Santorum.

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Written with contributions from Richard Piatt.

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