Clinton's aides contended that her strength with blue-collar voters — already demonstrated in primaries in Ohio, Pennsylvania and Indiana — makes her the more electable candidate in the fall.
"After tonight, we will have one more proof point, if you will, that Hillary Clinton is the strongest candidate Democrats can nominate," said Ann Lewis, an aide to the former first lady. "We're going to go back starting tomorrow and talk to those superdelegates who are still uncommitted and say, 'You know what? She is the candidate who expands the electoral map.' You look at West Virginia, you look at Kentucky, you look at Arkansas, you look at Tennessee. You look at what's at stake and that's a very powerful argument."
Clinton arranged a meeting with superdelegates for Wednesday.
She won at least 15 of the 28 delegates at stake in West Virginia, with 13 more to be allocated.
That left Obama with 1,875.5 delegates, to 1,712 for Clinton, out of 2,025 needed to clinch the nomination at the party convention in Denver this summer.
The delegate tally aside, the former first lady struggled to overcome an emerging Democratic consensus that Obama effectively wrapped up the nomination last week with a victory in the North Carolina primary and a narrow loss in Indiana.
He picked up four superdelegates during the day, including Roy Romer, former Democratic Party chairman.
"This race, I believe, is over," Romer told reporters on a conference call. He said only Clinton can decide when to withdraw, but he added: "There is a time we need to end it and direct ourselves to the general election. I think that time is now."
Clinton and Obama briefly shook hands on the Senate floor Tuesday after interrupting their campaigns for a few hours to vote on energy-related bills.