Barack Obama met with several potential running mates as part of an economic discussion with Democratic governors Friday morning, fueling speculation about whom he'll pick to balance the ticket.

At least 16 Democratic governors were invited to attend the event in Chicago. Among them were New Mexico Gov. Bill Richardson, Pennsylvania Gov. Ed Rendell, Kansas Gov. Kathleen Sebelius and Ohio Gov. Ted Strickland -- all mentioned as possible vice presidential picks.

The governors used the forum to discuss border security, job loss and energy conservation.

Obama also swiped at his GOP rival, John McCain, for supporting the summer gas tax holiday, which he called a "gimmick," and for supporting lifting the federal ban on offshore oil drilling.

"The notion that our energy policy would be to go before the oil company executives who are making $11 billion a quarter and say to them 'here's our answer, we're going to open up our coastline' ... It makes absolutely no sense at all," Obama said.

The meeting comes as Obama's vice presidential vetting team continues to hold interviews on Capitol Hill, even after one of the team members, Jim Johnson, stepped down following allegations about questionable loans he received.

Michigan Rep. Carolyn Cheeks Kilpatrick told The Associated Press she met with the remaining team members -- Caroline Kennedy and Eric Holder -- on Wednesday, and that they indicated former Sens. John Edwards and Sam Nunn are on Obama's list of potential running mates.

Kilpatrick said she made several suggestions during the 45-minute meeting, including former Vice President Al Gore, Pennsylvania Rep. John Murtha and Strickland. Gore endorsed Obama on Monday.

"I asked them what type of person the senator is looking for. And they said in general, someone who could help him rebuild the country ... talking about change. How we reinvest in America, get people back to work and reinforce our education system and bring the jobs back," she said.

She declined to say which names were put forth by Kennedy and Holder. The prominent Democratic attorneys have been meeting with lawmakers on Capitol Hill to receive feedback on Obama's potential running mate.

When Kilpatrick said Gore was her personal choice, "they had a smile on their face. They have a list of candidates. I think I may have been the first to do that. They didn't say one way or the other."

She wasn't the only one to mention Gore.

Rep. Joe Baca, D-Calif., chairman of the Congressional Hispanic Caucus, met Wednesday with Kennedy and Holder. A former Hillary Clinton supporter, he offered Clinton's name but said he mentioned others, too. Those included Edwards, Sens. Joe Biden and Chris Dodd, Gore, Sebelius and Arizona Gov. Janet Napolitano.

He told FOX News that the choice is ultimately Obama's, and that he has to pick the candidate with the broadest appeal.

"I would say Bill Richardson is great as a Hispanic and that would be great for us, but is that the ticket that would get us across?" Baca asked. "We have to make sure we get across that finish line. You know we already crossed one hurdle, but we need to cross the other hurdle. And that’s the most important thing right now. To make sure that one will appeal to all segments in the community… and not just one segment of the community."

Edwards, a former North Carolina senator who was John Kerry's running mate in 2004, could help Obama appeal to white, working-class voters who largely favored Clinton in the primary and will be a critical voting bloc in the general election. The drawback is that Edwards was the vice presidential nominee on a losing ticket four years ago.

Edwards has said he is not seeking the vice presidency -- but hasn't ruled out accepting if asked.

"I'd take anything he asked me to think about seriously but, obviously, this is something I've done and it's not a job that I'm seeking," Edwards said last Sunday on ABC's "This Week."

Nunn would bring national security credentials to the ticket, having served as the longtime Armed Services Committee chairman. The former Georgia senator is a member of Obama's foreign policy advisory group.

But Nunn is no longer well-known nationally, having not been in office for more than a decade. He is a conservative Democrat who supported school prayer and opposed gays in the military, while Obama tends to have a more liberal viewpoint. Nunn will turn 70 in September.

Other lawmakers who have been briefed say there are about 20 names on the list Obama's team has been discussing. The list includes current and former elected officials and retired military generals, lawmakers have said.

Kilpatrick said most of the names she was asked about were in the Senate.

Obama's campaign announced Friday he will be campaigning with Clinton for the first time next week.

As for the governors meeting with Obama, Strickland has practically taken his name off the list.

The former Clinton supporter told NPR last week: “If drafted, I will not run; nominated, I will not accept; and if elected, I will not serve. ... So, I don’t know how more crystal clear I can be.”

FOX News' Chad Pergram and Bonney Kapp and The Associated Press contributed to this report.