Normally, the governors of Iowa and Kansas can slip into town without much fanfare. But as John Kerry (search) narrows his list of potential running mates, no profile is too small for Washington's favorite parlor game: Veepstakes.

Democratic Govs. Tom Vilsack (search) of Iowa and Kathleen Sebelius (search) of Kansas were in the nation's capital Wednesday to lobby for health insurance reforms, but their visit fueled speculation about Kerry's secretive process for selecting a vice presidential nominee.

"It's all a little odd," Sebelius said of the buzz surrounding the vice presidential search, dubbed "veepstakes" inside the Beltway.

Kerry and his advisers aren't talking, so everybody else is. People outside Kerry's inner circle are dropping the names of Vilsack, Sebelius and dozens of other politicians from both parties. Pundits compare the ritual to a political mating dance or high drama, with every public event a potential audition as Kerry eyes his future partner from afar.

The candidate took an afternoon off the campaign trail Wednesday to meet privately at the Capitol with advisers about the Democratic convention and, presumably, his vice presidential search. A few blocks away, Vilsack and Sebelius courted favor by denouncing President Bush's health care policies.

"Against the backdrop of the presidential campaign, you always have this subtle, sometimes overt, unofficial campaign for vice president," said Michael Feldman, an aide to former Vice President Al Gore.

Gore watched a parade of ambitious Democrats, including Kerry, angle for a spot on the 2000 ticket. Sen. Joe Lieberman of Connecticut eventually won the veepstakes that year, edging out Kerry and a third senator, John Edwards (search) of North Carolina, who again is running hard for the No. 2 job.

The last major candidate to bow to Kerry in the primary, Edwards has urged his fund-raising team to help fill Kerry's coffers. The Southerner has traveled the country on behalf of the nominee-in-waiting, accusing Republicans of creating two Americas -- one for the wealthy and one for everyone else.

A recent Associated Press poll conducted by Ipsos-Public Affairs suggested that a majority of registered voters want Kerry to pick Edwards.

Four years ago, few predicted that Bush would turn to Cheney, who headed his search team, or that Lieberman would become the first Jewish vice presidential nominee.

"The vice presidential nomination almost always doesn't go to the person who the people most expect. That doesn't bode well for John Edwards," said Steve McMahon, adviser to former Kerry rival Howard Dean.

One certain surprise would be Dean. His campaign against Kerry was bitterly fought, and advisers to the presidential candidate point to Dean's low approval ratings among voters. Still, the former Vermont governor is keeping hope alive by campaigning for Kerry in states where independent Ralph Nader (search) cut into Gore's vote four years ago.

Another former rival, Dick Gephardt, is well liked by Kerry and many of his advisers. "I'm happy to do whatever the Kerry campaign wants me to do to win this election," the Missouri congressman said in Michigan a month ago.

Among those also doing vice presidential spade work: retired Army Gen. Wesley Clark, Sen. Bob Graham of Florida, former Sen. Bob Kerrey of Nebraska, Gov. Mark Warner of Virginia and Gov. Bill Richardson of New Mexico.

The rumor mill churns out a steady stream of potential candidates, with Sen. John D. Rockefeller IV, D-W.Va., getting some buzz Wednesday.

It is bad form to lobby for the job, leaving hopefuls constantly searching for fresh and creative ways to describe their ambivalence. "There's a new one I am thinking of," Richardson said in April, "I would not accept at gunpoint."

A gun-shy Vilsack wouldn't even say whether he was meeting with Kerry on Wednesday, though advisers said he wasn't. Sebelius said she was meeting with only one member of Kerry's team -- her 23-year-old son, Ed, a Kerry staffer.

Her father, John Gilligan, was Ohio governor from 1971 to 1975. Sebelius said he lost re-election in part because voters thought he was flirting with the presidency instead of focusing on their interests.

Determined not to make the same mistake, the 56-year-old freshman governor said she plans to remain in Kansas -- a standard non-denial denial of vice presidential interest -- but says there's a bright side to speculation about Kerry putting a woman on his ticket.

"To have a number of women in the mix over and over again is good news," she said in an interview with The Associated Press.

The veepstakes game has become tiresome for Republican Sen. John McCain of Arizona (search), who has rejected Kerry's overtures about a bipartisan ticket.

Said Ron Klain, who worked for Gore in 2000: "You get limited glimpses at people and, ultimately, make a lifelong decision. Sometimes it works out, and sometimes it doesn't."