John Kerry (search) needs a wingman — or a wingwoman, for that matter.

After a near clean sweep in the Super Tuesday Democratic nomination contests, the Massachusetts senator has all but accepted his party's nomination to go head-to-head with President Bush in November. His chief rival in the past few weeks, North Carolina Sen. John Edwards (search), dropped out of the race Wednesday.

With Edwards' departure, now the big question for the presumptive nominee is who to pick as his vice-presidential running mate.

"No decisions have even been remotely made," said Kerry spokesman David Wade.

Kerry remained mum about potential political partners, describing it as a private and personal process. "I wouldn't just begin to throw names around," he told a Florida television station on Wednesday, adding that he wants someone capable of assuming the commander-in-chief position if need be, and someone he gets along with.

Naturally, Kerry will also be looking for someone who can bring certain strengths to the ticket that shore up Kerry's perceived weaknesses.

For more on the campaign, click to view Foxnews.com's You Decide 2004 page.

Regardless of Kerry's deliberation process, the Washington rumor mill is flying with speculation. Many pundits — as well as voters interviewed at the polls Tuesday — are hoping for a Kerry-Edwards ticket come November.

"No promises for the vice presidency right now, but I think a good feeling all around," said Fox News political analyst Susan Estrich.

"It looks like Edwards is the one who makes the most sense," added Florida Sen. Bob Graham (search), who dropped out of the presidential race a few months ago.

In his exit speech Tuesday, Edwards encouraged supporters to unite behind Kerry and said, "I intend to do everything in my power to make him the president of the United States."

Political insiders say if Kerry decided against Edwards as a running mate, he can argue that the North Carolina senator offers little help since Kerry beat him practically everywhere.

Lengthy Short List

Other names being floated around the Beltway are Missouri Rep. Dick Gephardt, New Mexico Gov. Bill Richardson, retired Army Gen. Wesley Clark — who also dropped out of the presidential running — and Graham. Iowa Gov. Tom Vilsak (search) and Indiana Sen. Evan Bayh (search) also may be in the mix.

Some political observers suggest New York Sen. Hillary Rodham Clinton (search), who endorsed Kerry on Wednesday, may be the right woman for the job.

Outside of the political field, Kerry may want to consider someone with economic experience to send a message of fiscal responsibility to Wall Street. Possibilities include Fannie Mae chairman and CEO Franklin Raines, who was President Clinton's budget director, or Robert Rubin, former Clinton Treasury secretary.

Fox News political analyst and former Republican House speaker Newt Gingrich said Kerry has to decide what region the majority of his support comes from and pick a running mate from that area.

"If he could talk her into it, I think the strongest vice-presidential candidate, without any question, would be Senator Clinton," Gingrich said. "People either love her or hate her. That's what conventional wisdom is. I believe she is one of the two most competent Democrats in politics, and she's married to the other one."

By the time the Democratic conventions come around, "if Kerry is way behind [Bush], it will be Edwards or Clark, if it's close, it may be Hillary," said Fox News political analyst and former Clinton political adviser Dick Morris.

A Kerry-Clinton ticket, however, could play to Republican charges that the Democratic Party is too liberal.

Graham, who could help deliver Florida to the Democrats and avoid another 2000 presidential election debacle, endorsed Kerry on Wednesday.

Asked whether he would wish to participate in vice presidential process. Graham said he would do anything within reason to get Kerry elected.

When asked if that's a 'yes' — Graham just smiled.

"He's got to decide not only on who he's most comfortable with but who he feels can bring electoral votes to achieve victory," Graham told Fox News.

When asked if Kerry called him soon to ask him to be his No. 2, Graham said: "I think it's very important George Bush not serve another term in the White House … we need to have a new president, John Kerry, and I'll do whatever I can to help him become the next president."

Richardson, who could give Kerry a hand winning the Latino vote, has repeatedly said he's happy with his gubernatorial position.

The Winnowing Process Begins

Just hours after cruising to victory on Tuesday, Kerry began laying the groundwork for selecting a No. 2.

Kerry aides met with DNC staff Wednesday to discuss the party's plans to integrate its apparatus with Kerry's operation. The plans call for Kerry naming a "general election director" who would oversee the DNC's activities for the November contest.

Jim Johnson, a prominent Washington Democrat, will lead the selection process. Johnson, vice president of a merchant-banking firm, once worked for former Vice President Walter Mondale (search).

Senior Kerry camp advisers said their boss could choose a nominee well before the Democratic nominating convention in his hometown of Boston in July.

But some political experts cautioned Kerry against rushing into a decision.

"I don’t know if there's any advantage to identifying the running mate early on ... there are frankly considerations of personal chemistry," Don Fowler, former chairman of the Democratic National Committee, told Fox News. "I think that will be done deliberately and systematically in the interest of the party and the American people."

Opponents say it doesn't matter who runs with Kerry in November.

"I don't think the No. 2 selection's going to make much of a difference. I think it's going to be George Bush against John Kerry," said Fred Malek, former campaign manager for George H.W. Bush.

Fox News' Carl Cameron, Catherine Loper, Amy Sims and The Associated Press contributed to this report.