Former Sen. John Edwards

"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," said Edwards, a former North Carolina senator who exited the race in January.

"But I think the one thing that she has to be careful about ... going forward, 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," he said in a taped interview broadcast on CBS' "Face the Nation."

Clinton says she's staying in the race despite losing to Obama by a wide margin in North Carolina and barely winning in Indiana, which helped cement his status as the front-runner. She touts her overall electability in a general election and, pointing to demographics, recently told USA Today in an interview:

"There was just an AP article posted that found how Senator Obama's support among working — hardworking Americans, white Americans, is weakening again, and how the, you know, whites in both states who had not completed college were supporting me."

Some accused Clinton of reintroducing race into the campaign. Edwards seemed to give her a pass.

"She's in a very tough, very competitive race that's been going on a long, long time. And you know, she didn't probably — I'm sure she feels like she didn't choose her words very well there," he said.

"What I think is, at the end of the day, when this is over — and I think it is likely, certainly, at this point, that Senator Obama will be the nominee — that the Democrats will unite. We'll all be behind our nominee. And we'll be out there campaigning our hearts out," Edwards said.

David Axelrod, Obama's chief campaign strategist, disputed Clinton's assertion.

Axelrod said Obama and Clinton split Indiana voters who make $50,000 a year or less, and that Obama performed better among non-college-educated voters there. He said the same was true in North Carolina. Both states voted last week.

"The words weren't well chosen, but the thesis was wrong," Axelrod said on "Fox News Sunday.

Edwards, meanwhile, said he "might" still endorse a candidate, but "I don't think it's a big deal, to be honest with you."