(CNN) -- Sen. John McCain claimed victory in Florida's Republican primary, and Sen. Hillary Clinton took the state's Democratic contest Tuesday night.

John McCain celebrates his win in the Florida Republican primary. more photos »

The results in the Republican race might have delivered a fatal blow to the campaign of former New York Mayor Rudy Giuliani, who was a distant third as results came in Tuesday night.

Two GOP sources with direct knowledge of Giuliani's plans said he will drop out of the race and endorse McCain at an event in California on Wednesday.

While Giuliani didn't say he was withdrawing from the race, he did speak of his campaign in the past tense at one point.

"I'm proud I ran a positive campaign," he told supporters. "I ran a campaign that was uplifting." Watch how Giuliani reacted to the results »

With 97 percent of Republican precincts reporting, McCain held a 36-31 percent lead over former Massachusetts Gov. Mitt Romney. Giuliani had 15 percent of the vote, followed closely by former Arkansas Gov. Mike Huckabee who held 14 percent. See what the results mean »

A top campaign official from McCain's camp has been in "ongoing discussions" with Giuliani's campaign about endorsing McCain's candidacy, a GOP official familiar with talks told CNN Tuesday. Watch what happened to Giuliani's campaign »

A source close to Giuliani confirmed that discussions were taking place and said there is talk among the staff that an endorsement could come Wednesday in California. The source said McCain and Giuliani need to talk, but "we are working to make it happen."

"Tonight, my friends, we celebrate. Tomorrow, it's back to work," McCain said as he claimed victory. "We have a ways to go, but we're getting close, and for that, you all have my profound thanks." Watch McCain claim victory »

A Florida win gives McCain all 57 of the delegates at stake.

Romney took aim at McCain Tuesday night, putting the Arizona senator on the hot seat for failures in Washington, his criticisms of President Bush and for going from the military directly into Congress.

"Washington is fundamentally broken," Romney said. "We're not going to change Washington just by sending the same people back just to sit in different chairs." Watch Romney thank his supporters »

McCain, who cultivates an image as a maverick, has been in the senate for four terms after two terms as a U.S. congressman.

Huckabee told his supporters he was "playing all nine innings of this ball game." Audio slideshow: Candidates react to the Florida results »

"Even the Cardinals occasionally have a rough inning, but they know how to win championships," he told a crowd in Missouri. Watch Huckabee say he's just getting started »

With about 97 percent of Democratic precincts reporting, Clinton had 50 percent of the vote. Illinois Sen. Barack Obama was in second with 33 percent, and former North Carolina Sen. John Edwards was in third with 14 percent.

The Democratic vote may have little impact on the presidential race, however, because the party's national leadership said it would not allow Florida's delegates to participate in the national convention because of a squabble over scheduling.

Republicans penalized the state as well, but took away only half of their 114 delegates.

CNN political analyst Bill Schneider said earlier a Florida victory for McCain would be significant because it would be a way for him to prove he has the support of his party's base.

Florida is a closed primary, which means that only registered party members may vote in their own party's primary. McCain won primary contests in New Hampshire and South Carolina, thanks in part to the backing of independent voters who cast ballots in the Republican contests.

Clinton claimed victory despite party sanctions stripping the state of its convention delegates, thanking supporters even though she and other candidates did not campaign there.

"I am thrilled to have had this vote of confidence that you have given me today," Clinton told supporters. "I promise you I will do everything I can to make sure not only are Florida's Democratic delegates seated, but Florida is in the winning column for the Democrats in 2008." Watch how Clinton won in Florida »

Clinton has called on the Democratic Party to formally lift sanctions on the state.

Robert Gibbs, communications director for Obama campaign, downplayed the Florida results and got a dig in at Clinton.

"Mike Gravel is going to get the same number of delegates as Clinton," Gibbs said, referring to the former Alaska senator who has yet to earn a single percentage point in earlier contests.

Gibbs said he thought the results would have little effect on the race heading into Super Tuesday.

"You can't gain momentum in a state that everyone but Hillary Clinton pledged not to campaign in," Gibbs said.

Turnout was high for the Democratic race even though no delegates were at stake. Florida Sen. Bill Nelson said about 2.5 million voters cast ballots, and nearly 400,000 people cast early or absentee ballots ahead of the primary. See scenes from Florida's Republican race »

Donna Brazile, who managed former Vice President Al Gore's presidential bid, said many Democrats were likely to turn out to vote on a state constitutional amendment that would limit property tax increases and expand homestead exemptions.

"People are very afraid this will cut public services, cut back education," said Brazile, a CNN analyst. "So the Florida Education Association and all of the unions are spending millions of dollars to get voters to turn out."

The economy is overwhelmingly the top issue for voters in Florida's primary, according to early exit polls.

Among Republicans and Democrats, the economy dwarfed other issues affecting their vote. Forty-seven percent of Republicans said the economy is the most pressing issue, as did 55 percent of Democrats.

The primary calendar played in Florida's favor. Other than Republican caucuses in Maine this weekend, Florida is the last contest before the coast-to-coast primaries and caucuses on February 5, known as Super Tuesday.

McCain, Romney and the three other candidates engaged in a civil debate in Florida on Thursday night. But since Friday, the McCain and Romney camps, and the candidates themselves, have fired away at each other over the war in Iraq, the economy, illegal immigration and border security, campaign finance reform and the environment. Watch scenes from the 2008 battle for the White House »

And the negative attacks are not just occurring at campaign events and being reported by the media.

"It's also raging in paid advertising on TV and radio. Romney has spent $30 million on TV ads in Florida this year," said CNN political correspondent Dana Bash. That's five times as much as the McCain campaign, which is now using less expensive radio commercials to directly question Romney's credibility on the economy.

Huckabee has campaigned in Florida, but he's also spent time stumping in some of the Southern states that will vote on Super Tuesday.

Rep. Ron Paul of Texas is also concentrating on the February 5 states. E-mail to a friend

CNN's Bill Schneider, Paul Steinhauser and Alexander Mooney contributed to this report.

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