WASHINGTON (CNN) -- Many voters in Saturday's Republican contests showed they're not yet ready to support Sen. John McCain as their party's nominee while Sen. Barack Obama cut into Sen. Hillary Clinton's lead in the race for Democratic delegates.

Obama claimed victory in Louisiana, Nebraska and Washington on Saturday, as well as in the Virgin Islands.

"The stakes are too high and the challenges are too great to play the same old Washington game with the same old Washington players and expect a different result," Obama told a hugely supportive crowd of Democrats at the Jefferson-Jackson dinner in Richmond, Virginia.

"People want to turn the page. They want to write a new chapter in American history." Watch Obama rally in Virginia »

Clinton has 1,100 delegates and Obama has 1,039, according to CNN calculations.

Obama leads in pledged delegates -- 908 to 877 -- but Clinton's superdelegates -- 223 to 131 -- give her the overall lead.

"If I'm your nominee, you will never have to worry that I will be knocked out of the ring, because I do have strength and experience to lead this country, and I am ready to go toe-to-toe with Sen. McCain whenever and wherever he desires," Clinton said Saturday. Watch Clinton address supporters »

On the Republican side, Mike Huckabee upset front-runner McCain in Saturday's Republican contests. What do the results mean? »

The former Arkansas governor beat McCain in Kansas nearly 3-1.

Huckabee also took Louisiana, narrowly edging out McCain, according to CNN projections.

With both Huckabee and McCain falling short of the 50 percent mark, the 20 delegates will be allocated at next Saturday's Louisiana state GOP convention.

In Washington state, the state Republican Party declared McCain the winner.

Huckabee's Saturday wins show that Republicans are not necessarily falling in line behind McCain, the Republicans' presumptive nominee.

In Louisiana, exit polls showed that a majority of conservatives rejected the Arizona Republican. Only 34 percent of conservatives voted for McCain compared with 50 percent who voted for Huckabee, according to exit polls.

"People across America are gravitating toward our campaign and realizing that there is still a choice. And that's what we've said all along, that this race is far from being over," Huckabee said after the first results came in. Watch what Huckabee says about the results »

Obama and Huckabee have done well in caucus states like Iowa, where grass-roots efforts are more likely to have greater influence.

Obama also picked up a boost in Washington with the endorsement of the state's governor, Christine Gregoire.

Saturday's races marked the first contests without former Massachusetts Gov. Mitt Romney, who suspended his campaign Thursday.

But Huckabee faces a daunting challenge. McCain has a significant lead in the delegate count after Super Tuesday. Huckabee has 217 delegates to McCain's 714, according to CNN calculations.

Even if Huckabee wins every remaining state with 50 percent of the vote to McCain's 40 percent, McCain would still be the nominee.

"The other scenario... if he kept winning by large margins could he keep John McCain short of the line? That is a more probable scenario, but still an unlikely scenario," said CNN chief national correspondent John King.

"I know the pundits, and I know what they say: The math doesn't work out," Huckabee said Saturday morning at the Conservative Political Action Conference in Washington. "Well, I didn't major in math, I majored in miracles. And I still believe in those, too."

A senior McCain adviser said the campaign was not surprised by the results in Kansas.

"There are more caucus states we will probably lose, but our campaign is focusing on a transition from front-runner to nominee," he said.

McCain spent part of Saturday making calls in a bid to shore up conservative support for his campaign, according to CNN's Dana Bash.

Huckabee scored wins in the Southern states of Alabama, Georgia, Tennessee, and his native Arkansas on Super Tuesday, and social conservatives in Louisiana might mobilize behind him and send a message to McCain.

Huckabee pulled off a win in the Iowa caucuses, the product of a grass-roots movement, and both Kansas and Washington are caucus states.

Huckabee said Saturday that the $250,000 his campaign had raised online in 24 hours was a sign of the health of his presidential effort.

Louisiana, still suffering from Hurricane Katrina, could be a key political state this year -- something not lost on both Democratic campaigns as they drum up last-minute votes. Watch the Democratic candidates campaign »

On the Republican side, Huckabee was in Kansas on Friday. He attended rallies in Olathe, Wichita, Topeka and Garden City.

McCain, meanwhile, held a national security roundtable in Norfolk, Virginia, and later traveled to Wichita, Kansas. Afterward, it was off to Seattle. E-mail to a friend

CNN's Sean Callebs and Alan Silverleib contributed to this report.

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