"It's time he make that decision," John Podesta, Clinton's campaign chairman, said during an appearance Wednesday on MSNBC's "Andrea Mitchell Reports."
Biden, who has been publicly mulling a White House bid for weeks, skipped the first Democratic presidential debate. On Wednesday, he said that he was "proud" of the performance from the five candidates on stage in Las Vegas. 
But he hasn't said whether he will jump into the race, leaving many to speculate that Clinton's strong debate performance Tuesday night has closed the door for him to launch a late bid.
Clinton's campaign appears to be shifting its tone after the debate, saying that while Biden should have been given space to grieve the loss of his son Beau in May, he needs to make a decision about the 2016 race.

"I think he's been through a tremendous tragedy. And we've been respectful about that, and I think he deserved the space and the time to think that through about whether it was best for him to begin this new challenge to try to mount a presidential campaign," Podesta said Wednesday on MSNBC. 

"But I think the time has come for a decision so that at the next debate, if he does decide to get in, there will be six podiums on the stage."