WASHINGTON — Sens. Barack Obama and John McCain have begun taking steps toward choosing their running mates.

McCain has a head start in the "veepstakes," with Obama still fighting off Sen. Hillary Rodham Clinton. The GOP candidate will be getting better acquainted with three potential picks during a holiday gathering at his home this weekend, while Obama's team is still in the early stages of compiling background information on possible running mates.

Former Fannie Mae CEO Jim Johnson is overseeing the early vetting for Obama, Democratic officials say. Johnson did the same job for Democratic nominees John Kerry in 2004 and Walter Mondale in 1984.

Many of the people Johnson checked for Kerry may be likely candidates for Obama's consideration. Those names included Sen. Clinton, New Mexico Gov. Bill Richardson, anti-war Republican Sen. Chuck Hagel of Nebraska and Kerry's eventual choice, former North Carolina Sen. John Edwards.

Obama refused to acknowledge Johnson's role when he was asked about it in the Capitol yesterday.

"I haven't hired him. He's not on retainer. I'm not paying him any money. He is a friend of mine. I know him," Obama said.

Johnson has been a top fundraiser for his campaign.

"I am not commenting on vice presidential matters because I have not won this nomination," Obama said.

The Democratic officials who revealed Johnson's role spoke on a condition of anonymity, saying that Obama has insisted that the process be kept quiet.

McCain is hosting at least three Republicans mentioned as potential vice presidential running mates at his Sedona, Ariz., home this weekend — Florida Gov. Charlie Crist, Louisiana Gov. Bobby Jindal and former Massachusetts Gov. Mitt Romney.

An aide said it's a social event with more than two dozen guests not meant for veep vetting. Still, the socializing is a prime opportunity for would-be running mates.

Before heading off to Arizona, Romney announced he was forming the "Free and Strong America" political action committee that will allow him to travel the country on political business and support like-minded candidates.

The vice presidential speculation about McCain's possible choice has been going on for months, fueled in part by the candidate himself.

Since sewing up the nomination in March, McCain has campaigned with prospective running mates, including Romney, Crist, Utah Gov. Jon Huntsman and former Arkansas Gov. Mike Huckabee.

Last month, McCain said he was in the "embryonic stages" of the search with a list of about 20 names.

At one point, McCain let slip that as he learns about the process of picking a running mate, he'd like to speak to A.B. Culvahouse, who has been involved in vice presidential searches before and served as counsel to President Reagan from 1987-1989. Several Republicans close to the campaign said that while McCain and campaign manager Rick Davis are running the show, Culvahouse is involved in the process.

Obama is still engaged in an all-but-settled nomination campaign against Clinton, with three primaries left in Puerto Rico, South Dakota and Montana. The voting ends June 3.

Clinton spokesman Howard Wolfson said Obama's vice presidential selection process "is clearly premature in that he is not yet the nominee."

He also said the Clinton campaign didn't have a similar process under way and there had been no discussions with the Obama people about her becoming the Illinois senator's No. 2.

Some in the party are calling for Obama to pick Clinton, but others say that couldn't work after their long and heated campaign against each other.

Other possible options are governors such as Janet Napolitano of Arizona, Kathleen Sebelius of Kansas and Tim Kaine of Virginia; foreign policy experts including former Georgia Sen. Sam Nunn, Connecticut Sen. Chris Dodd or Delaware Sen. Joe Biden, or other senators such as Missouri's Claire McCaskill or Virginia's Jim Webb.

Obama could look outside the party to people such as Hagel or independent New York Mayor Mike Bloomberg. Or he could look to one of his prominent supporters such as former Sen. Tom Daschle of South Dakota or 2004 vice presidential nominee Edwards. He also could try to bring on a Clinton supporter such as Indiana's Sen. Evan Bayh or retired Gen. Wesley Clark.

House Speaker Nancy Pelosi indicated yesterday that she thought the timing was right for a veep search, even as she was careful not to play favorites.

"This election is right around the corner, and a new president will be sworn in in a matter of months," said the California Democrat.

Asked if she'd be interested in the running mate spot, she replied, "Are you kidding? Being Speaker of the House is the best job in the world. Why would I want to be No. 2?"