WASHINGTON (CNN) -- Sen. Hillary Clinton used her big win in West Virginia on Tuesday to make her case that she has a better chance of beating the Republicans in the general election.
Sen. Hillary Clinton told supporters Tuesday that she believes she's the stronger candidate.
"I am more determined than ever to carry on this campaign," she told supporters in Charleston, West Virginia.
"I am in this race because I believe I am the strongest candidate. ... I can lead this party to victory in the general election if you lead me to victory now."
With half of the results in, Clinton was ahead of Sen. Barack Obama by a margin of more than 2-1.
Clinton has faced calls to drop out of the race because she trails Obama in delegates won, states won and the popular vote this primary season.
Clinton also now trails Obama when it comes to the support of superdelegates, and her campaign is $20 million in the red.
Howard Wolfson, Clinton's communication director, said the New York senator is "in until the very end." Watch Clinton say she's determined to go on »
"We think we're going to be the nominee. We're going to make our case to the superdelegates," he said.
In an e-mail to supporters, the Clinton campaign called West Virginia a "tremendous victory."
"It's clear that the pundits declaring this race over have it all wrong. The voters in West Virginia spoke loud and clear -- they want this contest to go on."
Clinton's win won't do much to cut into Obama's lead: West Virginia had just 28 delegates at stake, and those will be awarded proportionately.
Her campaign argues that she can catch Obama in the popular vote by turning out the vote in the remaining five contests.
Clinton has also continued to tout her electability, saying she's more fit to go up against Sen. John McCain, the presumptive GOP nominee, in November.
"I'm winning Catholic voters and Hispanic voters and blue-collar workers and seniors, the kind of people that Sen. McCain will be fighting for in the general election," Clinton said earlier. Watch campaign aide discuss Clinton's electability »
Reiterating a point she has made frequently while campaigning in West Virginia, Clinton pointed out Tuesday that no Democrat has won the White House since 1916 without winning West Virginia.
Bill Clinton won there in 1992 and 1996. George W. Bush took the state in 2000 and 2004. Watch analysts predict what comes after West Virginia »
In addition to West Virginia, Clinton's campaign points to other swing states she has won -- like Ohio and Pennsylvania -- as they try to woo superdelegates to their side.
"They have changed some minds, but more minds have been changed right now in favor of Sen. Obama," CNN contributor Donna Brazile said.
Obama surpassed Clinton in the race for superdelegates Monday. Clinton led by more than 100 at the beginning of the year.
Obama appeared to be looking ahead of Tuesday's vote toward a general election fight with McCain as he campaigned in Michigan and Missouri. Read how the candidates are turning their attention to the fall »
"There's a bipartisan tradition in foreign policy that we should try to recapture. Unfortunately, John McCain is not going to provide that," Obama said in Cape Girardeau, Missouri.
Both Obama and Clinton have softened their attacks on each other in recent days. Obama has turned his attacks to McCain, and Clinton spoke favorably of Obama in her victory speech Tuesday.
Still, exit polls from West Virginia indicate a strong division among Democrats.
Almost as many of Clinton's West Virginia supporters would vote for McCain as would for Obama, the polls show.
If Obama were the Democratic nominee, 36 percent of Clinton supporters would vote for him in the fall, the polls found.
But 35 percent said they'd cast their vote for McCain instead.
A bare majority of his West Virginia supporters -- 51 percent -- said they would back Clinton in the fall, but 31 percent said they'd vote for McCain.
After West Virginia, the campaign trail moves to Kentucky and Oregon, which vote in one week. Clinton is expected to do well in Kentucky, but Obama is the favorite to win Oregon.