"Many Democrats are having a sense of déjà vu and are turning to the person who was there before," Princeton's Zelizer said. "On the other [hand], they want to contain him. They're very nervous. They don't want him to overshadow the president. That's the danger with former presidents, especially with Bill Clinton, given his ability to really dominate the public stage."
A majority of Americans continue to rate Clinton well on his job performance, despite the scandals that marked his presidency, from 1993 to 2001. In an ABC News/Washington Post in 2008, 55 percent of those polled expressed a favorable view of him personally.
Clinton is not one to back down from his views, whether they are popular or not, a point that makes many Democrats nervous. He savored in campaigning for his wife in her presidential run despite the friction between him and some of her aides.
"You do get the sense privately he's chomping at the bit to get after and help the Democrats right now," Zelizer said. "He's kind of one step away from the campaign train, always."
He was bothered when Al Gore didn't make him the center of his 2000 presidential campaign, and although he accepted it, he never forgot, Zelizer said.
"He played ball but there's always this resentment he had that Democrats don't fully appreciate what he offers and what he thinks," he added.
Clinton is unlikely to slow down any time soon. His friends said he was on a conference call about aid to Haiti until right before the surgery Thursday, where doctors placed two stents in one of his coronaries.
"If anything, this will get President Clinton more energized," longtime Clinton friend Terry McAuliffe said on "Good Morning America" today. "To him, sleeping is taking time away from something he could be doing to help somebody."
Clinton is also likely to continue to be called on to unweave complicated situations, as was the case with health care. And even if he may not be front and center of key discussions in Washington, his legacy still remains alive with the cadre of former Clinton administration officials now working in the White House.
"I think the importance is not so much in his hands-on influence on Washington as it is the indirect influence of his legacy through people," Russell Riley, a presidential scholar at the University of Virginia's Miller Center of Public Affairs, said. "Rahm Emanuel wouldn't be where he was had it not been for his experience in the Clinton administration."