WASHINGTON — Barack Obama and John McCain have begun taking quiet but purposeful steps toward choosing their running mates, fresh signs that the Democratic nomination fight is over and the presidential race is rapidly moving toward the Obama-McCain general election matchup.

McCain has a head start in the "veepstakes," with Obama still fighting off never-say-die 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, and that allows for a quick start. Johnson won't be starting from scratch, since he did the same job for Democratic nominees John Kerry in 2004 and Walter Mondale in 1984.

Many of the people Johnson checked for Kerry will 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 The Associated Press asked the Illinois senator about it in the Capitol Thursday.

"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."

The Democratic officials who revealed Johnson's role spoke on a condition of anonymity because 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 — former Massachusetts Gov. Mitt Romney, Florida Gov. Charlie Crist and Louisiana Gov. Bobby Jindal. An aide said it's a social event with more than two dozen guests not meant for veep vetting. Still, the event 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 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 veeps, including Romney, Crist, Utah Gov. Jon Huntsman Jr. and former Arkansas Gov. Mike Huckabee.