Two of those people said he is leaning toward entering the race. Still, they caution that family considerations remain the overriding concern and would be the reason he doesn't run. His wife, Dr. Jill Biden, has said that should the vice president launch a bid for the Oval Office, "of course" she would "be on board."

Even if Biden decides to seek the Democratic nomination before the party's first debate on Oct. 13, he likely would not participate, sources told CBS News.

They said he'd need time - perhaps a couple of weeks - to put together the foundations of a campaign and raise money looking ahead to several ballot deadlines. States like New Hampshire, Texas and Florida have deadlines beginning in November.