As he prepares to leave office next year, he sometimes sounds closer to Mr. Obama than his own party.

Mr. Schwarzenegger does not rule out an Obama administration post, and urges the president to press ahead with a health care overhaul that tracks his own failed push on the issue in California.

“People say, ‘Well, he has taken on too many things,’ ” Mr. Schwarzenegger said of Mr. Obama. “But if he doesn’t take on the too many things, then they say, ‘Well, he hasn’t taken on enough.’ ”

Contrasting his approach with that of Sarah Palin, the conservative celebrity who has quit the Alaska governorship, he concluded, “I would never give up.”