"It's a new day, it's a new state, it's a new election," Clinton told reporters in West Virginia on Wednesday.
Clinton said that she was the strongest candidate to go up against presumptive Republican nomineeand vowed to fight on.
"I'm staying in this race until we have a nominee," Clinton said. "I obviously am going to work as hard as I can to become that nominee."
Obama beat Clinton soundly in North Carolina and fell just short in an Indiana cliffhanger, a rebound for the Illinois senator that presented Clinton with fast-dwindling chances to deny him the Democratic presidential nomination.
CBS News has learned several top advisers are suggesting to Hillary Clinton that she stay in the race through West Virginia, Kentucky and Oregon and then bow out in two weeks, reports CBS News chief White House correspondent Jim Axelrod.
One Clinton loyalist told CBS News senior political correspondent Jeff Greenfield, "I can't see the math that gets her to the nomination-neither can anyone else."
Putting her money troubles into clearer focus, Clinton's campaign said Wednesday that sheover the past month. Earlier this year, she gave her campaign $5 million.
But even as she sought to rejuvenate her campaign, Clinton suffered the loss of a high-profile backer - former Sen. George McGovern - who switched his support to Obama and urged the New York senator to drop out of the race for the good of the party.
Obama spent Wednesday off the campaign trail at home in Chicago, but expected to travel later in the week to Oregon, where he appears to hold the advantage, and then head to the Appalachian coal-states of West Virginia and Kentucky, where Clinton seems to have the edge.
Reluctant to give John McCain a free pass until the Democratic nomination is settled, Obama is considering adding general election swing states to his schedule, his campaign strategist, David Axelrod, said.
Clinton showed no public signs of easing her pace. The campaign added a noon Wednesday appearance in Shepherdstown, W. Va., to her schedule. On Thursday, she planned to campaign in West Virginia, South Dakota and Oregon.
Clinton backers appeared on early morning television programs to stress that she was still in the race and to urge party leaders and elected officials known as superdelegates not to flee to Obama.
"This candidacy and this campaign continues on," Clinton communications director Howard Wolfson said Wednesday on CNN.
According to the latest CBS News count, Obama has secured 1,844 of the 2,025 delegates needed to clinch the nomination, his campaign finally steadying after missteps fiercely exploited by the never-say-die Clinton.
His campaign dropped broad hints it was time for the 270 remaining unaligned superdelegates to get off the fence and settle the nomination.
In a counter to Wolfson, Obama communications director Robert Gibbs said: "The delegate math gets exceptionally harder for Senator Clinton every day"
In a memorandum to superdelegates, Obama campaign manager David Plouffe reminded them of the delegate math necessary to secure the nomination. He said Clinton would need to win 68 percent of the remaining delegates to win - an extremely unlikely scenario, made harder by her poor performance Tuesday.
"With the Clinton path to the nomination getting even narrower, we expect new and wildly creative scenarios to emerge in the coming days," Plouffe wrote. "While those scenarios may be entertaining, they are not legitimate and will not be considered legitimate by this campaign or millions of supporters, volunteers and donors."
It was in the superdelegate arena - even more than in the scattered primaries left - that the Democratic hyperdrama was bound to play out.
Clinton vowed to compete tenaciously for West Virginia next week and Kentucky and Oregon after that, and to press "full speed on to the White House."
But she risked running on fumes without an infusion of cash, and made a direct fundraising pitch from the stage in Indianapolis. "I need your help to continue our journey," she said.
And she pledged anew that she would support the Democratic nominee "no matter what happens," a vow also made by her competitor.
But her campaign schedule belied any immediate reconciliation. West Virginia holds its primary on Tuesday. Kentucky and Oregon hold their contests a week a later. Puerto Rico is scheduled for June 1 followed promptly by Montana and South Dakota on June 3.
Her campaign is making the case that those contests are crucial to her and will press Democratic party officials to resolve disputed contests in Michigan and Florida, which she won but whose results the party voided because the primaries were held ahead of the schedule set by Democratic Party rules.
Obama, addressing supporters in North Carolina Tuesday night, pivoted away from his contest with Clinton and made a general election appeal that singled out his biography and his call for a new brand of politics. Still, his message also had a partisan pitch.
"This primary season may not be over, but when it is, we will have to remember who we are as Democrats ... because we all agree that at this defining moment in history - a moment when we're facing two wars, an economy in turmoil, a planet in peril - we can't afford to give John McCain the chance to serve out George Bush's third term," he said.
McCain has been running a general election campaign for weeks. He has reached out to independent voters and sought to secure his conservative base, as he did Tuesday with a speech on his vision of the judiciary. He was scheduled to deliver a speech Wednesday on curbing the international exploitation of children.
The Obama-Clinton contest has been polarizing, protracted and often bitter, hardening divisions in the party, according to exit polls from the two states.
A solid majority of each candidate's supporters said they would not be satisfied if the other candidate wins the nomination.
Fully one-third of Clinton's supporters in Indiana and North Carolina went beyond mere dissatisfaction to say they would vote for McCain instead of Obama if that's the choice in the fall.
Obama scored a convincing victory of about 14 points in North Carolina, where he'd been favored. Clinton squeezed out a narrow margin in Indiana after a long night of counting.
Racial divisions were stark.
In both states, Clinton won six in 10 white votes while Obama got nine in 10 black votes, exit polls indicated.
It was a slightly better performance than usual by Clinton among whites, while Obama's backing from blacks was one of his highest winning percentages yet with that group.
Clinton fell short of the Indiana blowout and the North Carolina upset that might have jarred superdelegates into her camp in a big way.
They have continued trickling toward Obama despite the fallout over his former pastor's racially divisive remarks and Clinton's win in Pennsylvania two weeks ago.
The impact of a long-running controversy over the Illinois senator's former pastor, the Rev. Jeremiah Wright, was difficult to measure.
In North Carolina, six in 10 voters who said Wright's remarks affected their votes sided with Clinton. A somewhat larger percentage of voters who said the pastor's remarks did not matter supported Obama.
Obama and Clinton both planned to campaign in the next primary states starting Thursday, after a day in Washington. Obama headed to Chicago after his Raleigh speech before coming to the capital.