"It doesn't mean she'll actually pick Obama," said Trippi, who now works as a CBS contributor.
Trippi said Sen. John Kerry's campaign did the same thing in 2004 with Edwards, putting out the word in Iowa and other states that it was considering Edwards for vice president.
"People just said, 'Great. I can vote for John Kerry and I get John Edwards, too,'" Trippi said. In the end, Kerry did choose Edwards as his running mate for their failed 2004 bid against President Bush.
"Clinton's comment is designed to give permission to Obama supporters to go ahead and support Clinton," agreed Democratic pollster Margie Omero, who isn't affiliated with either campaign.
Other Democratic strategists argue that the "dream ticket" is really more of a fantasy, given the intense and sometimes bitter nomination battle.
"This is tactical silliness," said Democratic strategist Anita Dunn, who has worked with Obama in the past. "This is going to be a tough campaign that's going to go on for at least several more weeks."
Historically, bitter primary opponents have sometimes put aside their animosity to join forces for the general election.
John F. Kennedy made peace with his primary opponent and eventual vice president Lyndon B. Johnson. George H.W. Bush assailed Reaganomics as "voodoo economics," then came onboard as Reagan's vice presidential pick.
Dunn also said Clinton's remark about being at the top of the ticket denotes some chutzpah.
"It's highly unusual for the person in second place to be talking about putting the other person on their ticket as vice president," she said.
On a conference call with reporters Wednesday, Clinton's chief strategist Mark Penn demurred when asked whether Clinton would be open to being Obama's vice presidential pick.
"I'm not going to interpret her remarks beyond what they are," Penn said. "We are super focused on winning the nomination, and we're not really commenting or going beyond that."
The "dream ticket" scenario was also floated before the multistate Super Tuesday votes in February. "Would you consider an Obama-Clinton or Clinton-Obama ticket going down the road?" asked CNN's Wolf Blitzer during a CNN debate in January.
"Well, there's a difference between those two," Obama laughed. "But her service to this country has been extraordinary. And I'm glad that we've been walking on this road together."
"Well, I have to agree with everything Barack just said," Clinton said.
A March ABC News/Washington Post poll found 36 percent of Democratic voters polled said that if Obama wins, he should choose Clinton as his running mate; 11 percent preferred Edwards and 3 percent preferred New Mexico Gov. Bill Richardson. Former Vice President Al Gore and Delaware Sen. Joe Biden each got 1 percent.
Women were much more likely than men to say Obama should choose Clinton, 41 percent to 28 percent. During the 2008 campaign, Edwards, the 2004 Democratic vice presidential pick, maintained that he was running for president, not vice president. But Edwards' supporters argue he would be a great pick.
"He has said no, but I would certainly hope that he would serve, if asked, as vice president or attorney general," Trippi said. "There are a lot of us who hope he will get asked and that he will serve."