(CNN) -- Republican Sen. Saxby Chambliss claimed victory Tuesday in the Senate race in Georgia against Democrat Jim Martin, killing Democratic hopes of gaining enough seats to halt filibusters.

Voters "delivered a strong message that conservative Georgian values matter," Chambliss said.

"People all around the world truly had their eyes on Georgia, and you have delivered tonight a strong message to the world that conservative Georgian values matter," Chambliss said.

"Now comes the hard work."

Chambliss said he is prepared to work with Barack Obama when he becomes president, but not in all matters.

"When he wants to raise your taxes, when he wants to tinker with the Second Amendment, when he wants to make proposals with respect to health care that is going to take your choice of choosing your doctor away form you, then I'm going to be the 41st senator to stand up and say no." Watch Chambliss give his victory speech »

Chambliss' remarks followed a concession speech by Martin.

"Tonight, the voters of Georgia have spoken," he told supporters. "I accept the decision that has been made." Watch Martin give his concession speech »

The election is playing off the results of November 4, when Chambliss failed to win a majority of the vote in a three-person race.

Democrats have so far picked up seven Senate seats in this year's election, with the Republican seat in Minnesota still undecided.

In Minnesota, freshman GOP Sen. Norm Coleman topped his Democratic challenger, Al Franken, by just 215 votes, triggering an automatic recount that will extend well into December.

Had Democrats taken the Georgia and Minnesota contests, they would have reached their pre-election goal of controlling 60 Senate seats, which would be a filibuster-proof majority. A filibuster is a move by the minority party in the Senate that brings the chamber to a standstill by blocking votes on legislation. Watch CNN's John King report on the runoff »

Chambliss won a plurality on Election Day, but Georgia state law requires a majority -- 50 percent plus one vote. Because of the inclusion of a third-party candidate, Chambliss fell just shy of that threshold, forcing a runoff election. See results from Tuesday's runoff election

Chambliss promised to be a firewall against the Democrats in Washington, while Martin aligned himself with Barack Obama and the president-elect's message of change. Both sides brought in big-name surrogates to help motivate base voters.

Sarah Palin, the Alaska governor and former Republican vice presidential nominee, teamed up with Chambliss at four campaign events across Georgia on Monday. Watch more on Palin's return to the trail »

"You Georgians are going to have the opportunity to determine the direction this country is going to take," Palin said during a campaign rally in Perry, in south Georgia.

"This election is that important, and I know come tomorrow night, Georgians are going to speak, and Georgia's going to speak with a loud and clear voice. We want to make sure we have at least 41 Republicans in the United States Senate to make sure that we shape bad legislation, or kill bad legislation."

Chambliss had urged Palin to come to Georgia and help him get out the conservative vote.

Sen. John McCain returned to the trail to campaign with Chambliss just nine days after losing the presidential election to Obama.

Other former presidential hopefuls -- including former Arkansas Gov. Mike Huckabee, former Massachusetts Gov. Mitt Romney and former New York City Mayor Rudy Giuliani -- also have hit the trail for Chambliss in the past month.

Giuliani, Huckabee and Romney could all make another presidential bid in 2012, and Palin could be joining them. iReport.com: Did you vote in Georgia?

Martin also received some major-league help. Both former President Bill Clinton and former Vice President Al Gore have separately teamed up with him.

And while Obama resisted Martin's invitation to come down to Georgia in person, the president-elect did lend his voice to a 60-second radio ad that ran for more than a week.

And many who worked in Georgia for Obama during the general election campaign assisted Martin.

On Monday, Martin teamed up with Rep. John Lewis and other prominent Georgia Democrats before ending the day at a rally at the State Capitol in Atlanta with rapper Ludacris.

Martin called Palin's four campaign stops Monday a sign of desperation for Chambliss, adding that "bringing Sarah Palin is not going to help him, because the voters of Georgia want someone who will stand up for them in Washington; someone who understands their issues."

Analysts said turnout was crucial to the outcome of this election, raising the question of whether big-name surrogates make a difference.

"Generally they can help boost turnout, because of all the media attention," said Bill Schneider, CNN's senior political analyst.

"Turnout in a runoff election is often very low compared to a presidential election, and each side needs to get as many of their voters to the polls as possible."

This is Georgia's first runoff election for a U.S. Senate seat since 1992, when incumbent Democrat Wyche Fowler won a plurality of the vote on Election Day but lost the runoff election to Republican Paul Coverdale.

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