The Clinton camp had previously said such a ticket might be a good idea -- with Obama in the veep spot.
But as the primaries come to an end and Clinton's chances of overtaking Obama's delegate lead dwindle, the former U.S. president has joined the Hillary-for-Veep bandwagon, ABC News' chief Washington correspondent George Stephanopoulos reported.
"He is definitely talking it up, making no secret it would be a strong ticket for Barack Obama," Stephanopoulos reported on "Good Morning America" this morning.
Has Clinton Earned No. 2 Spot?
Bill Clinton believes that his wife has "earned the offer of vice president," Stephanopoulos said.
"You're also seeing Clinton supporters talking it up as well, like Sen. [Diane] Feinstein of California," he said.
Hillary Clinton bolstered her credentials for a spot on the ticket in recent weeks with lopsided primary victories in West Virginia and Kentucky, demonstrating her strength among bedrock Democratic groups like blue-collar workers and women.
There are three primaries left -- Puerto Rico on June 1 and South Dakota and Montana on June 3 -- and Clinton publicly shows no sign of conceding the nomination to Obama. The two camps are currently wrangling over the disputed delegations of Florida and Michigan, which Clinton hopes to settle in her favor.
"Barack Obama will be under pressure to at least give this serious consideration," Stephanopoulos said.
'Dream Ticket' or Nightmare?
But other top Democrats are downplaying the possibility of a dream ticket in an apparent effort to give Obama support for choosing his own running mate.
Sen. Ted Kennedy, D-Mass., who has endorsed Obama, played down the possibility of an Obama-Clinton ticket in a recent interview with Bloomberg's Al Hunt.
"I don't think it's possible," Kennedy told Hunt on Bloomberg TV. "I would hope that [Obama] would," Kennedy explained, "also give consideration to somebody that has -- is in tune with his appeal for the nobler aspirations of the American people. And I think if we had real leadership -- as we do with Barack Obama -- in the No. 2 spot as well, it'd be enormously helpful."
The Democratic group VoteBoth, which is dedicated to an Obama-Clinton or a Clinton-Obama ticket, didn't much like Kennedy's analysis.
"We respect Sen.Kennedy's opinions about what is best for the party, but we think that the millions of Democrats who have voted for Barack Obama and Hillary Clinton have something to say, too. Why stop at having a nominee who has the support of 51 percent of Democrats when we could have a 'Dream Team' ticket that has won 100 percent?" spokesman Sam Arora said in a statement.
House Speaker Nancy Pelosi also expressed similar doubts.
"We will have a dream ticket and it will contain one of them," the California Democrat said on "This Week With George Stephanopoulos."
Pelosi, who has officially remained neutral, was even more blunt during an earlier news conference on Capitol Hill.
"I just don't think it's going to happen," she said, saying her political gut told her such an arrangement between two former rivals would be "impossible."
"Take it from me, that won't be the ticket," Pelosi stated emphatically.
The Candidate's Thoughts
Obama gave a noncommittal answer when pressed on the subject Thursday while campaigning in Boca Raton, Fla., saying he would be like Abraham Lincoln and consider his rivals for top administration jobs.
"I want to know if you'd consider everybody who is a possible help to you as a running mate," a Pompano Beach voter asked. "Even if his or her spouse is an occasional pain in the butt."
The candidate initially laughed off the query but then replied, "My goal is to have the best possible government. And that means me winning. So, I'm very practical in my thinking. I'm a practical guy."
On the other side of the aisle, Arizona Sen. John McCain will host several Republican vice presidential contenders at his home in Sedona, Ariz., this Memorial Day weekend.
Gov. Bobby Jindal of Louisiana, Gov. Charlie Christ of Florida and former Gov. Mitt Romney of Massachusetts have all been invited to spend some leisure time with the presumptive Republican presidential nominee.
McCain campaign senior adviser Charlie Black insists the gathering is purely social.
"It has nothing whatsoever to do with the vice presidential selection process," Black said, dismissing speculation that it is a running mate audition by noting that would be "pretty awkward" to have all of the contenders together at the same time.
McCain has assembled, according to Stephanopoulos on today's "Good Morning America," a list of 20 potential vice presidential candidates. That list includes New York City Mayor Michael Bloomberg, a Democrat who became a Republican and then, earlier this year, became an independent.
Bloomberg, a multimillionaire who considered a third-party candidacy, has met with McCain and Obama in the course of the campaign.
*Are you a politics junkie? We have more political gems on our four political blogs written by a White House insider, PhD and Eyewitness News reporters.