As supporters of Sen. Hillary Clinton wage a public campaign urging Sen. Barack Obama to select her as his running mate, some Democrats are resisting the idea, with former President Jimmy Carter saying it would be the "worst mistake" possible.
The Clinton camp put the brakes on the idea today in a statement to the media.
"While Senator Clinton has made clear throughout this process that she will do whatever she can to elect a Democrat to the White House, she is not seeking the vice presidency, and no one speaks for her but her," the Clinton campaign said in a statement. "The choice here is Senator Obama's and his alone."
The presumptive Democratic nominee Thursday said he has not spoken to Clinton since learning she will endorse him.
"I am very, very grateful for her support, and I'm looking forward to having a conversation with her. We haven't had the opportunity yet; we're both catching our breaths, and sort of sorting through all the things we have to do organizationally," he told reporters on his campaign plane flying to Brisol, Va.
Asked if there is any possibility he'll pick Hillary Clinton as his running mate, he 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."
Obama said at the right time and place they will appear together, "Until that time where we have a conversation I don't want to speculate or characterize anything, you know, there will be a time and a place where she and I, I'm sure, appear together and talk about how we're gonna work together."
In an interview on CNN Thursday, Obama said, "I think everybody just needs to settle down," he said. "This will be my final counselor when I'm making decisions in the White House. And I want to make sure that I get it right," Obama said.
Obama Weighs Pros and Cons
Clinton brings to the table her broad support from white blue-collar workers, women, Hispanics and older voters, which Obama had trouble holding in large numbers during the primaries.
The former first lady is also tied to a failed bid for universal health care, her 2003 vote authorizing the Iraq War and eight years of the Clinton administration, not to mention the former president himself.
"A lot of Obama supporters believe having Senator Clinton on the ticket undercuts their message of change," ABC News' George Stephanopoulos said on "Good Morning America" Thursday.
One of Clinton's most vocal surrogates suggested that Clinton would outshine Obama on the campaign trail.
"The rule for the vice president is make sure you never upstage the president," Gov. Ed Rendell, D-Pa., said Wednesday in an interview. "It's rule one. You know, Hillary Clinton in some ways couldn't help but upstage, even if she was trying not to."
It's unclear whether former President Bill Clinton would submit to a vetting process that would delve into his business dealings and the millions he has made since leaving the White House.
Then there's the relationship between the presumptive nominee and the former president, who in January accused the Obama campaign of "playing the race card" on him, likened Obama's South Carolina primary win to Rev. Jesse Jackson's wins there in 1984 and 1988 and referred to Obama's Iraq policy as a " big fairy tale."
Carter: 'Worst Mistake'
Carter, who endorsed Obama, cautioned against a joint ticket.
"I think it would be the worst mistake that could be made. That would just accumulate the negative aspects of both candidates," Carter said in an interview with the British newspaper The Guardian.
"If you take that 50 percent who just don't want to vote for Clinton," Carter said, "and add it to whatever element there might be who don't think Obama is white enough or old enough or experienced enough or because he's got a middle name that sounds Arab, you could have the worst of both worlds."
But some high-profile Republicans cheered on the "dream team."
"The dream team is polling better than any other team," said Mary Matalin, a Republican strategist and former principle advisor to Vice President Dick Cheney. "She does augment in very real ways Senator Obama's weaknesses."
Obama: Clinton 'Tough'
Obama, in his first public campaign event since Clinton agreed she would concede the race to him Saturday, offered praise for the former first lady.
"Obviously, we've had a pretty exciting 48 hours here," Obama told a crowd in Bristol, Va., today, calling the field of presidential candidates outstanding but "none more outstanding than Senator Hillary Rodham Clinton."
"I congratulate her on her great achievement, and I know I'm a better candidate because I ran against her. She's tough," Obama said.
Clinton has told supporters that she's ambivalent about being chosen for vice president — that she's "open" to it, but just as happy to return to the Senate.
Clinton Supporters Lobby For VP Slot
But some of her most loyal backers are publicly urging Obama to make Clinton his vice presidential candidate.
Leading the charge is Lanny Davis, the senator's longtime friend and Yale Law classmate, who launched a petition Wednesday night urging Obama to ask her to be his vice presidential candidate.
"We write to urge you to select Sen. Hillary Rodham Clinton to be your choice for vice president because we believe that she would be, by far, the most qualified and strongest candidate to be your running mate," reads the petition, located at womenforfairpolitics.com.
Making a case to Obama directly, it reads: "Your selection of a vice presidential candidate may make the difference between victory and defeat."
Robert L. Johnson, the founder of Black Entertainment Television and a prominent Clinton confidant, said in an interview that she was "absolutely ready" to talk to Obama about the No. 2 slot and would take it if offered.
'It's Just Not Done'
Some Democrats find the effort distasteful and predict it will backfire.
"I think this notion that you can campaign for vice president or you can draft somebody for vice president, or you can force somebody on the ticket is ridiculous and irresponsible," said Bill Carrick, a Democratic strategist.
"There's no case where somebody on their own, or supporters who are acting independently, have run a campaign and lobbied successfully to get somebody on a ticket," Carrick said. "It's just not done and the people who've done it in the past, it's backfired."
Obama said Wednesday he had tapped three people, including President John F. Kennedy's daughter, Caroline Kennedy, to lead his search for a vice presidential nominee, and has said he wants to meet with Clinton.
"I think it's very important for me to meet with her and talk to her about how we move this party forward," Obama told ABC's Charlie Gibson Wednesday. "My main goal is to make sure that the party is unified."
'Deeply Personal Decision
But after an often bitter, five-month-long primary battle, Obama may be reluctant to choose her for personal reasons.
"At the end of the day, it really is a deeply personal decision about identifying a partner the nominee wants to work with, not just for the next five months, but for four or eight years," said Chris Lehane, a Democratic strategist who worked on former Vice President Al Gore's 2000 presidential election campaign.
ABC News' Sunlen Miller who is covering the Obama campaign contributed to this report.