Image: Hillary Clinton
Craig Ruttle  /  AP
U.S. Sen. Hillary Rodham Clinton, D-N.Y., left, speaks at a news conference on children's health care in New York, Thursday, Aug. 30, 2007.
updated 8/31/2007 4:34:12 PM ET 2007-08-31T20:34:12

Hillary Rodham Clinton has already had to forgo one potential running mate _ her husband.

Asked by talk-show host David Letterman if Bill Clinton could serve as her vice president should she be elected to the White House, the former first lady acknowledged that he could not.

"Believe me," she joked, "he looked into that."

She also remarked that if the Constitution didn't forbid a president from a third term, "he might be running."

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Such easy banter marked Clinton's seventh appearance on "The Late Show," which was celebrating its 14th anniversary on CBS. She first appeared on Feb. 14, 1994, when Letterman's mother, Dorothy, interviewed her briefly from the Winter Olympics in Norway.

On Thursday's show, Clinton recounted a summer in Alaska during which she donned boots and an apron to gut salmon with a spoon.

"Best preparation for being in Washington that you can possibly imagine," she joked.

Clinton talked shop, too, discussing the need for campaign finance reform, how to pull troops out of Iraq and the importance of caring for wounded veterans. She said that while resistance to a female commander in chief has diminished, it hasn't disappeared.

"I think it's not so much that people don't think a woman can do the job, it's just that we've never done it before," she said. "I'm not running because I'm a woman; I'm running because I think I'm the best-qualified and experienced person who can do the job. But I know that it's a big deal that I might be the first woman president."

Clinton also read a "Top Ten List" of tongue-in-cheek campaign promises, including No. 3: "We will finally have a president who doesn't mind pulling over and asking for directions."

Copyright 2007 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

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