However, Edwards said, "The math is very, very hard for her," as Sen. Barack Obama continues to lead in pledged delegates (and now in superdelegates). "The problem is, I think, you can no longer make a compelling case for the math."
Edwards, D-N.C., told Face The Nation host Bob Schieffer that his own reasons for pulling out of the race for the White House came out of both a recognition that he would not accumulate enough delegates to secure the nomination and that his continued candidacy would likely prolong the selection of a nominee.
"It's a hard judgment to make," he said. "The overwhelming likelihood was I would not be the nominee. And I believed, that if I got out of the race, it would accelerate the process of one person pulling away. Well, I was obviously dead wrong about that!"
When asked about the position Clinton is in right now, and the calls by many for her to withdraw from the race, Edwards said, "I think it's a judgment that she has to make. And I think she's in a very, very tough place.
"I have to tell you, I'm different than a lot of people. I actually admire some of the strength and fortitude that she's shown. I know how hard it is to get up and go out there every day, speak to the media, speak to crowds, when people are urging you to get out of the race. I mean, it's a very hard place to be in. But she's shown a lot of strength about that.
"I think the one thing that she has to be careful about - and she doesn't need my advice, she knows this full well - is that, if she makes the case for herself, which she's completely entitled to do, she has to be really careful that she's not damaging our prospects, the Democratic Party, and our cause, for the fall."
Clinton campaign chairman Terry McAuliffe reiterated the Senator's position that she would not pull out of the race until all states have had a chance to weigh in. "We still have 7 million Democrats yet to vote," he said, alluding to primaries in West Virginia and Kentucky, among others.
But he also admitted that with more superdelegates announcing their preferences, it was likely that the nominee would be decided in June after primary voting concludes, and the fate of Michigan and Florida delegates is resolved.
McAuliffe also dismissed concerns that the long primary season will create long-lasting divisions within the party. "This is a very close race, and we need to get everybody together at the end," he said.
"I disagree with a lot of these Democrats today that are saying we won't be unified. We will be very unified. George Bush has been the greatest unifying force in the history of the Democratic Party. He has brought us all together. We will be together."
Also appearing on the show was Jim VandeHei, executive editor of Politico, who said there are those within the Clinton campaign who admit that they need a miracle - or, perhaps a scandal.
"They need an imponderable," he said. "They know they can't just win it by collecting enough popular votes. ... But as long as she stays in there, anything can happen. And this is a family that has had a political career that's been built upon sort of defying expectations and coming back when people thought it was not possible to come back.
"Who knows? Politics is completely unpredictable. And as long as she's in it for another six weeks or four weeks or whatever it will be, she has a chance. And she just wants that chance."
Read the full "Face the Nation" transcript here.