Hillary Clinton and Barack Obama embrace after the CNN Democratic Debate Thursday (Photo Credit: Getty Images)
(CNN) - Many Democrats call it a "dream ticket." Clinton/Obama or Obama/Clinton - in whichever order.
And after the civil affair at Thursday's debate, it seems like more of a possibility - at least, perhaps, more of a possibility than it was in the last several weeks when the two candidates were locked in a heated back-and-forth on the campaign trail.
But both Democrats artfully dodged the notion of running together in a general election when CNN’s Wolf Blitzer raised the possibility.
"Well, obviously there's a big difference between those two," Obama said to laughter regarding whether his name or the New York senator's is on top.
"But, look, let me say this," Obama continued. "I respect Sen. Clinton. I think her service to this country has been extraordinary. And I'm glad that we've been walking on this road together and that we are still on that road.We've got a lot more road to travel. And so I think it's premature for either of us to start speculating about Vice Presidents - I think it would be premature and presumptuous."
Clinton also would not say whether she thought it was a possibility.
"This has been an extraordinary campaign, and I think both of us have been overwhelmed by the response that we have engendered, the kind of enthusiasm and intensity that people feel about each of us," she said. "And so, clearly, we are both dedicated to doing the best we can to win the nomination, but there is no doubt we will have a unified Democratic Party."
Related: Watch Clinton and Obama discuss the potential of sharing the Democratic ticket
- CNN Producer Alexander Mooney