John Kerry (search) woke up Wednesday the clear front-runner in the Democratic presidential race, with primary wins in Arizona, Missouri and Delaware, and caucuses victories in North Dakota and New Mexico.

"For the second time in a few days, a New England patriot has won on the road," Kerry told a roaring crowd of supporters in Washington state Tuesday night, referring to the New England Patriots' Sunday Super Bowl win.

"We will take nothing for granted, we will compete everywhere and in November, we will beat George W. Bush."

John Edwards captured the South Carolina primary Tuesday and barely lost Oklahoma to retired Army Gen. Wesley Clark (search) — the two are now squaring off, with each having a single win apiece, lagging far behind Kerry.

"We won and we won big," Edwards told Fox News Wednesday. "It was a big night for us."

Clark announced his first win to supporters at 11:35 p.m. EST, saying, "I couldn't be prouder of your support in this first election that I've ever won."

Asked how he can stop front-runner Kerry's momentum, Edwards told Fox News:  "I'm going to keep doing what I've been doing...talking about what voters are concerned about, instead of just the politics... how to bring hope back to people..."

In New Mexico, Kerry won 42 percent of the vote with 100 percent of caucus sites reporting, Clark was second with 21 percent; former Vermont Gov. Howard Dean (searchhad 16 percent. Edwards won 11 percent. Of about 75,000 ballots cast in the state's first Democratic presidential caucus, 23,000 votes were mail-in ballots sent in by Jan. 26, the day before the New Hampshire primary.

Connecticut Sen. Joe Lieberman (search), who did not win a primary or caucus in nine races, dropped out Tuesday night.

"The judgment of the voters is now clear and I want to congratulate John Kerry and John Edwards on the victories they have won today," Lieberman said, thanking the other candidates for "their willingness to serve our country and for all that each of them has already contributed to this campaign and our great Democratic Party."

With 100 percent of the vote counted in Delaware, a state Lieberman had called a must-win, Kerry won 50 percent compared to Lieberman and Edwards, who tied with 11 percent.

Kerry also broke the 50-percent barrier in Missouri, winning 51 percent. Edwards won 26 percent in Dean took 9 percent of the vote in Missouri.

The Massachusetts senator won Arizona with 43 percent of the vote and held his second place finish in South Carolina with 30 percent of the vote. Edwards won 45 percent of the vote in South Carolina.

Kerry, a Vietnam veteran, made a special point to thank the nation's veterans for supporting him.

Pointing out that Bush didn't acknowledge veterans in his State of the Union address, Kerry said: "I pledge when I am president, I pledge to those who have worn the uniform of our country and those who wear it today, that I will be a champion for them in the Oval Office and that patriotism is defined by never forgetting those who wore the uniform of our country."

Edwards said his double-digit win against Kerry in South Carolina was "way beyond my expectations and way beyond the polls."

"South Carolina's a place where it's a real test for being able to win the South, which Democrats have to do," and for winning rural and black voters, Edwards told Fox News after his win there.

But asked if they would run together in a general election, both Kerry and Edwards said it was "inappropriate" to do anything but to continue fighting for the nomination.

Prior to Tuesday's races, Kerry was winning the race for delegates, having leapfrogged Dean by winning unpledged "superdelegates." Now, Kerry is expected to have won about 10 percent of the total 2,161 delegates needed for the nomination..

In Tuesday night's contests, 269 pledged delegates were at stake. Candidates must receive at least 15 percent support in the caucuses to be considered viable. If a candidate's support doesn't meet that threshold, caucus participants have the option to throw their vote behind another candidate.

Click here for the exit poll.

What Happened to Dean?

After finishing in third place in Arizona and Missouri and reaching the 15 percent threshold needed for delegates in New Mexico, Dean was expected to win some delegates heading into Saturday's races in Michigan and Washington. Dean told supporters in Tacoma, Wash., that he is in the race for the long haul.

"I think the momentum has clearly shifted ... but ultimately issues are going to decide this and the issue is, do you want a different kind of American than we have right now," Dean said.

For more on the campaign, click to view Foxnews.com's You Decide 2004 page.

Dean's campaign has suffered from a shortage in funds following a spending spree before the Iowa races, and he has been forced to lay off staff and cut back on advertising.

But while the candidate blamed the media for crowning him too soon and rivals for using desperate tactics to torpedo his campaign, analysts said Dean had trouble transferring his cult-like support into votes and sometimes talked without thinking of the political consequences.

"Howard Dean had a great recruitment message for Democrats and new voters to get them into the party and feel part of the process," said Democratic consultant Jenny Backus. "I think Democrats are past wanting to be recruited and they are now looking at electability instead of inspiration."

Dean said he was going to keep going regardless of Tuesday's outcomes.

"We're going to keep going and going and going and going and going, just like the Energizer bunny and you know why? Because we're going to pick up some delegates tonight and this is all about the most delegates in Boston [at the Democratic National Convention] in July and it's going to be us," he said.

He continued to take slaps at the candidates he considers "Washington insiders."

"I'm the only candidate that really represents fundamental, institutional change in this country, which is I think what this country really needs," Dean told Fox News Tuesday night when asked about his future campaign strategy.

"The Washington senators are perfectly nice people but they're not going to deliver," he added, referring to Kerry and Edwards.

But political experts were skeptical of Dean's forecasts.

"You can talk about being the Energizer bunny but where will he go to?" asked Fox News political analyst Susan Estrich. "I don't think Howard Dean is going to make threshold in a lot of these states. He's got a real tough night tonight yet his rhetoric is stronger than ever."

Lieberman aides now say with Dean effectively out of the race, it will be up to Kerry, Edwards and Clark to make sure the party is not branded as weak on economic and national security.

The Right Stuff

Fox News exit polls show that Edwards' win in South Carolina was attributable to his message on the economy and jobs. Fifty-seven percent of voters there said Edwards has the most qualities that could help them. But 80 percent said they would be satisfied if Kerry won the nomination.

In Missouri, Kerry won 75 percent of the votes among people who counted electability as their top consideration at the polls. Edwards won 12 percent, while Clark took 6 percent and Dean had 3 percent.

Among those who counted experience as their top quality in a candidate, Kerry won 72 percent of that vote compared to 11 percent for Clark, 5 percent for Dean and 4 percent for Edwards.

Kerry also won 42 percent of the voters who put the candidates' caring about people like them as their most important quality. Edwards won 31 percent of that group, Dean won 9 percent and Clark won 4 percent.

In Delaware, Kerry also won big among those who placed the economy and health care as their top issues in the race. He won 48 and 56 percent respectively.

The Campaigns Continue

Kerry's campaign will begin TV ads in Virginia and Tennessee on Wednesday. The Edwards campaign will concentrate on Tennessee and Virginia and will beef up resources in Wisconsin.

Estrich said Dean's decision not to drop a lot of money in advertising on Michigan, with its 128 unpledged delegates, is not a bad decision, especially since she still expected the race to come down to Kerry and Edwards.

"Michigan is a mixed system, You can either come in for what they call a firehouse caucus you show up and vote or you can go on the Internet and vote, so it's hard to predict. Nobody is putting money on the air in Michigan because it would probably be wasted," Estrich said.

Clark is going to Tennessee to campaign on Wednesday and his spokesman said his camp has the finances and the staff to continue.

"We intended to win and we've got plenty of money. We've got strong organization all over the country but we are going to win today," Clark told reporters before the race.

But analysts say Clark's campaign may be finished.

"His Waterloo was in New Hampshire," said Weekly Standard Editor Fred Barnes."Even narrowly winning a race in Oklahoma, he will crow about it ... I think his campaign is over with."

"Kerry has stolen his thunder with the veterans, and I think that's the end of his campaign," added National Public Radio national correspondent Juan Williams.

Fox News' Carl Cameron, Major Garrett, Catherine Loper and The Associated Press contributed to this report.