The names most mentioned are energetic, young governors, including Mark Sanford of South Carolina, Tim Pawlenty of Minnesota, Jon Huntsman Jr. of Utah, and Charlie Crist of Florida.
McCain, in a recent joint appearance with Crist, said, "I think there are many ways for him to serve the country."
On his program "This Week" today, ABC's George Stephanopoulos told Crist it seemed that McCain was hinting that he might be considering putting the Florida governor on his short list for vice president.
"Well, I'm considering being the best governor I can for the people of Florida," Crist parried.
As Stephanopoulos noted, that was hardly a categorical rejection of the suggestion.
Many Republicans think the party can win Florida without Crist on the ticket, but they are not so confident about Minnesota, and believe Pawlenty could help there.
"He could be a very inspired choice," said Sara Taylor, a former political director in the Bush White House, who also noted that the Republic convention is going to be in Minneapolis.
Another possibility from the Midwest is Rob Portman, a former congressman from Ohio, which is a hugely important swing state.
McCain recently called Portman "a great, great, great congressman and a great man."
Business executive Carly Fiorina is heading McCain's search for a running mate.
If Hillary Clinton is on the Democratic ticket, McCain may be tempted to choose a woman. Sen. Kay Bailey Hutchison of Texas and Secretary of State Condoleezza Rice have both been mentioned as potential vice presidential candidates if McCain is looking for a woman.
If the economy continues to be the top issue, however, McCain could even choose former GOP rival Mitt Romney, who has a successful background in the business world.
They may not like each other, but sometimes politics overrides personal antipathy. That's what happened in 1960 when John Kennedy chose Lyndon Johnson, when it was felt the Massachusetts senator needed someone from the South or the West to broaden the appeal of the ticket.
But McCain's friends say he is more likely to choose a running mate he actually likes than to make a decision based on politics alone.
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