"Until she decides that she can't win at the convention and makes a decision, it's going to stay open," Levin said on CBS's Face The Nation. "However, I think it's more than likely that within a week or two that Senator [Barack] Obama will have enough votes to claim that he's going to be the nominee."
However, with yesterday's ruling by Democratic Party officials over the disputed delegates from Florida and Michigan, Clinton advisor Mandy Grunwald said that Clinton still has a very strong case to make for the support of the party's superdelegates who will be the ultimate deciding factor.
"Over 17 million people have now voted for Hillary Clinton," Grunwald said, representing the "deepest and broadest coalition" needed to win in November.
She also warned of the sentiment voiced by some Hillary supporters at the outset of yesterday's meeting: "If a female candidate, the first successful one in history, goes into the convention leading in the popular vote and it's taken away from her, how do you think women are going to feel, heading into the November election?"
Avoiding an ugly convention battle, or a divisive general election turnout, is the main objective, said Sen. Claire McCaskill, D-Mo., who believes Clinton will "do the right thing, because the stakes are way too high for America.
"I have great confidence that Hillary Clinton will do what's right for our party and for our nation and for all those people out there that are hurting - and are going to keep hurting if we let four more years of George Bush in the White House. That's what we'd get with John McCain."
Gov. Ed Rendell, D-Pa,, concurs that Clinton would not jeopardize the party, but continued to back her as the candidate best able to succeed in the key battleground states in November.
"The polls make it clear that on the states that are necessary for us to win the Electoral College, Hillary Clinton is by far our strongest candidate in the fall," Rendell said. "What are we doing nominating the weaker of our two fine candidates? It makes no sense to me."
Nonetheless, Rendell thinks a joint ticket would "sweep the country," but it will only come about by Clinton and Obama coming together themselves.
"No politicians are going to be able to broker it," he told host Bob Schieffer. "The staffs, who have a little bit of animosity, as always is the case, can't be involved. I think Senator Clinton and Senator Obama have to sit down together and talk about the future of this country and talk about whether that is a viable option. It's up to the two of them."
Read the full "Face the Nation" transcript here.