Carol Moseley Braun (search), the only woman vying for the Democratic presidential nomination, pulled herself out of the crowded race Thursday and threw her backing behind rival Howard Dean (search).

Braun, a former U.S. senator from Illinois, ended her long-shot bid for president in Iowa, a crucial state that holds its caucuses Monday night. Dean once enjoyed a big lead in the Iowa polls but now finds himself in a statistical dead heat with three of his challengers — John Kerry (search), Richard Gephardt (search) and John Edwards (search).

"Gov. Dean has the energy to inspire the American people, to break the cocoon of fear that envelopes us and empowers President Bush and his entourage from the extreme right wing," she said in prepared remarks.

On Wednesday night, after news of Braun's decision became known, Dean told reporters that he welcomed her support.

"She's a principled person. We just hit it off. I like her a lot," the former Vermont governor said. "It's going to be a big help to us."

But Braun's endorsement — she was never expected to win the nomination, a fact her own campaign acknowledged — is expected to do little for Dean's campaign.

"In Iowa and New Hampshire, if you're calculating that Carol Moseley Braun's support is coming from African-American Democrats, there aren't a lot of those to be had in those two states," said David Corn, a Fox News political analyst and the Washington editor of The Nation. "I think a politician will say every endorsement helps, but none helps a great deal."

Dean may need all the help he can get. The latest tracking polls show Kerry, a Massachusetts senator, with a slim lead over the field.

"I hope we're building momentum. Obviously, that's what we're trying to do," Kerry said in Iowa Thursday. "I feel energy in the campaign out here. The crowds have been incredible, people are responding. But as I've always said, voters are going to decide this. … You've just got to keep working."

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Kerry has a one-point advantage over Dean and Gephardt, a Missouri representative. Following closely behind is Edwards, a North Carolina senator. In effect, there is a four-way statistical tie, given the margin of error in polling.

"They're all competitive, they're all pouring it on in the end game. It's a very close race," Des Moines Register political columnist David Yepsen told Fox News. Dean's "not getting a free ride anymore."

In other campaign news, politics is taking a dirty turn as the candidates head in to the final four days of recruiting votes for Monday.

Gephardt, for example, has suggested that Dean is a fake, and Dean has accusing retired Army Gen. Wesley Clark (search) of being a closet Republican.

Dean has also made statements such as: "Let's not kid ourselves about this — these guys are looking at the end of their careers if I win and they're going to do anything they can to stop me."

But all the catfighting may be taking its toll.

Iowa Democrats "don't like all this sniping among Democrats and … they desperately want to beat George Bush in November," said Bruce Reed, president of the Democratic Leadership Council (search).

"One thing candidates are definitely learning from this experience is voters seem much more interested in the positive, in what you're going to do rather than how angry you are and what you've been against."

Pointing out that Dean is losing support in polls, Reed said, "I think Dean's paying a price everywhere for a pretty negative campaign."

Neck and Neck

In the latest Reuters/MSNBC/Zogby poll, Kerry had edged the doctor-turned-politician and Gephardt for a slight lead in Iowa caucus polling, despite endorsements for Dean from former Vice President Al Gore and former presidential hopeful Bill Bradley.

After trailing Dean by as much as 11 points earlier in the week, Kerry now has 22 percent of the vote — a single-point lead over the previous front-runner, who is tied with Gephardt. Edwards makes it a four-man race with 17 percent. All other possible contenders have 3 points or less in Iowa.

The latest New Hampshire poll of 622 likely voters shows Dean continuing on his downturn, garnering 29 percent of the Democratic vote. The poll, conducted by American Research Group (search) from Jan. 12-14, shows Clark steadily catching up with 24 percent of the vote, Kerry with 15 percent and all others in single digits. Fifteen percent were undecided.

What's telling is that Clark has been steadily gaining on Dean — with Dean losing steam — throughout the week in this poll, and the career military officer has been picking up more support from women over 45.

And while an American Research Group pollster cautioned to not oversell Dean's drop and Clark's gain, he said that based on recent polls, Kerry's rise is definitely the story of the day.

"John Kerry has been gaining the support of undecided Iowans for the past week," added Michael Meehan, senior adviser for the Kerry campaign. "We're looking to get one of the three spots coming out of Iowa. ... John Kerry wants one of those spots to take to New Hampshire."

Other candidates say Iowa won't make or break their campaigns.

"This is a very fluid race," said Craig T. Smith, Lieberman's campaign manager.

Saying there has been a "deep erosion" in Dean support, Smith believes voters now "are taking a serious look at all these candidates."

"I think you'll see a huge amount of shifting in the polls in the next few weeks," he added.

Meanwhile, other campaigns are saying they will be victorious in Iowa.

"We're not even going to entertain the notion of losing in Iowa," said Steve Murphy, Gephardt's campaign manager, adding that his boss has strong support from labor groups, farmers and senior citizens, among others. "We are going to win here, we have the best organization by far. The way this race is shaping up right now is great for Dick Gephardt."

Stress in the Dean Camp

Dean was flying high after receiving Gore's endorsement. But Dean's comments suggesting that the United States is not a safer place after the capture of former Iraqi dictator Saddam Hussein and that Americans should not pre-judge Usama bin Laden have and the criticisms his rivals have been piling on has hurt.

"I think it's taking a toll," said Elaine Kamarck, former senior campaign adviser to Gore.

Even if Dean loses Iowa, "he is truly a national candidate — he will go all the way," she said. "Whereas the other candidates "really have to emerge in Iowa, otherwise they will fall back."

Iowa is the first test of whether Dean can "expand the electorate."

Dean has acknowledged a "tight" race, and his haggard campaign aides are setting new standards for Internet fundraising, Meetups and political Web blogging. But Iowa is an old-fashioned organizational ground war — not a high-tech hotbed for politics.

Dean is trying to maintain his front-runner status, and is conducting a five-day bus tour across Iowa. Two of his Hollywood supporters — actor Martin Sheen (search) and director Rob Reiner (search) — are in Iowa to help Dean make his final push toward caucus night.

Fox News' Carl Cameron and Kelly Wright contributed to this report.