WASHINGTON — Senator Clinton is using her overwhelming victory in West Virginia last night to make a direct appeal to the undecided superdelegates who have the power to hand her the Democratic presidential nomination.

Although the New York senator faces a near-impossible mathematical path to the nomination, she declared in unequivocal terms that she intends to stay in the race.

“I am more determined than ever to carry on this campaign until everyone has had a chance to make their voices heard,” she told cheering supporters in a victory speech last night in Charleston, W.Va.

“I want to send a message to everyone still making up their mind: I am in this race because I believe I am the strongest candidate to lead our party in November 2008 and the strongest president to lead our nation in January 2009,” Mrs. Clinton said, a statement aimed pointedly at superdelegates. “I can win this nomination if you decide I should.”

Mrs. Clinton’s lopsided margin of victory in the Mountain State was widely expected, but the numbers were nonetheless striking. With 69% of the precincts reporting, Mrs. Clinton led Senator Obama by 66% to 27%.

Despite the blowout, the former first lady is expected to earn a net gain of just 10 delegates out of the 28 at stake in West Virginia. Mr. Obama maintains a total delegate lead of more than 150, and his advisers expect that he will clinch a majority of pledged delegates next week in Oregon and Kentucky. Mrs. Clinton would then need superdelegates to decide virtually en masse to support her if she is to have any chance at victory.

With a high population of white, working-class voters and few African Americans, West Virginia had favored Mrs. Clinton all along, and Mr. Obama barely campaigned in the state. He did not even appear in West Virginia last night after spending the day in the general election battleground of Missouri.

Mrs. Clinton argued, however, that the state has been crucial to Democratic general election victories dating to 1916, and she used her win to bolster her case that she is the stronger candidate for the fall.

“The bottom line is this,” she said. “The White House is won in the swing states, and I am winning in the swing states.”

Mrs. Clinton should know very quickly whether her dominating victory yesterday will be enough to stem the tide of superdelegates who have headed Mr. Obama’s way in recent weeks. His campaign has announced 27 more endorsements from those party leaders in the last week alone. Four superdelegates declared their support for Mr. Obama yesterday, including a former Colorado governor and chairman of the Democratic National Committee, Roy Romer, who said he saw no chance for a Clinton comeback.

“The math is controlling,” he told reporters on a conference call. “This race, I believe, is over.”

The Clinton campaign yesterday was making every effort to argue that was not the case, even as a prominent supporter and adviser, James Carville, conceded in an appearance at a South Carolina college that it was a “great likelihood” that Mr. Obama would win the nomination.

The Obama campaign sought to walk a careful line between turning its attention to Senator McCain and the general election while not giving any impression that it was trying to force Mrs. Clinton from the race. His campaign manager, David Plouffe, told reporters that Mr. Obama would not make a declaration of victory even if he clinches a majority of pledged delegates next week.

The talk in large measure has turned from whether Mrs. Clinton can overtake Mr. Obama to speculation over what concession she may demand in exchange for her exit from the race and a smooth transition to the general election.

Would she seek or accept the vice presidential nomination? Is she looking for Mr. Obama to help her pay off her $20 million campaign debt, including more than $11 million that she loaned herself? Mrs. Clinton has made clear that she wants the disputed delegations from Florida and Michigan seated at the nominating convention in August, and she could seek a commitment from Mr. Obama on health care policy, which has been a central point of contention during the primary campaign.

“It could be a mixture of all of the above,” a Democratic consultant, Michael Goldman, said. A former senior adviser to the Dukakis presidential campaign, Mr. Goldman said his exception was the vice presidency, calling the idea of an Obama-Clinton ticket “disastrous.”

“You want to choose a vice president who brings you something that you don’t have,” he said, noting that in Mr. Obama’s case, the key missing attribute would be military experience.

The possibility of a joint ticket has sparked a spirited debate among party leaders, with some saying a “dream team” is the only way to unite a fractured Democratic Party, while others, such as the House speaker, Nancy Pelosi, arguing that the divisiveness of the primary had rendered such a pairing impossible.