June 6, 2008 -- A stealthy meeting Thursday night between former presidential rivals Barack Obama and Hillary Clinton is no longer a secret, but what they discussed — and whether they said the words "vice president" — remains a mystery.
Obama, D-Ill., returned to his Chicago home early this morning, hours after slipping away from his press entourage for a clandestine meeting with Clinton in Washington, D.C.
Clinton, D-N.Y., also eluded the press staked out in front of her Washington mansion to meet with Obama at the home of Sen. Dianne Feinstein.
Feinstein, D-Calif., an early Clinton supporter who has publicly made the case for an Obama-Clinton ticket, told reporters outside the Senate chamber Friday that the meeting took began at about 9 p.m. ET and lasted an hour.
Feinstein said Clinton called her "sometime in the late afternoon" Thursday to set up the meeting and both came with one staffer, but the conversation was just between the two of them in the living room of her Washington home.
"There were no press, no staff. They had one person from each campaign that was in my study separately and I guess the security people outside," Feinstein said. "They both left laughing."
"You all know what it's like," Feinstein said. "I mean, you go out and you have to make a statement to the press and everybody is critical of it and they just want an opportunity to meet together alone."
In a rare joint statement Thursday night, the two Democrats said only, "Senator Clinton and Senator Obama met tonight and had a productive discussion about the important work that needs to be done to succeed in November."
Robert Gibbs, Obama's campaign communications director, confirmed the meeting took place, but said, "I don't have details of the substance of the meeting."
"Sen. Obama had talked to Sen. Clinton … was eager to do it and begin the process, as we have over the last couple days, of uniting the party, bringing the candidates together," he said.
Gibbs said he does not know who asked for the meeting, but it was arranged through staff.
Clinton to Concede Amid 'Dream Ticket' Calls
Clinton will throw a huge rally on Saturday to mark the end of her attempt to make history by becoming the first woman to win a major party's presidential nomination, and will use that moment to formally concede and endorse Obama.
Gibbs indicated that Obama would not make an appearance with Clinton on Saturday.
"I don't anticipate that. The way we understand it is the event on Saturday — and rightly so — is for and about Sen. Clinton and the historic campaign that she ran," Gibbs said.
Sen. Charles Schumer, Clinton's New York colleague and a strong backer, told "Good Morning America" Friday that the secret meeting was not about the vice presidential slot and instead was "a good … first step in terms of uniting the party."
Schumer made it clear, however, that Clinton is willing to become Obama's veep and at one point he said, "I urge Sen. Obama to consider her very seriously."
"But on the other hand if he chooses someone else, she'll work just as hard for the party in November," Schumer said.
Nomination Fight Ends, Veepstakes Begins
Obama has said that he won't make a quick decision on his running mate.
Asked on Thursday if there was any possibility that he'd pick Clinton as his running mate, Obama said, "I have said before that Senator Clinton would be on anybody's short list. She is an extraordinary talent and a major leader in her party as she showed during this campaign. But I am not going to discuss who is being considered, how they're being considered. We're just not gonna talk about this anymore."
"He'll take his time," Schumer said. "He said to some of us, it's better to do it right than to do it quickly."
Schumer also defended Clinton against criticism that she should have promptly conceded on Tuesday night when Obama won the necessary number of delegates to lock up the Democratic presidential nomination.
"Hillary Clinton deserved her space," Schumer said. "She deserved a little time to put on paper what she wants to say to the American people."
He also indirectly suggested that some Clinton backers remain angry that she will not be the party's nominee and may not vote for Obama.
"Most of us who have been Hillary supporters, about all of us will line up firmly behind Barack Obama," he said.
ABC News' Z. Byron Wolf contributed to this report.