We caught up with Arnold Schwarzenegger and his daughter Christina Schwarzenegger as they left Cafe Roma in Los Angeles, California. The two left after eating lunch and were surrounded by handlers and staff. Christina talked on a cell phone while Arnold talked to a man in the group.

The Associated Press Reported that:

With Arnold Schwarzenegger’s governorship entering its final years and his ability to attract the spotlight intact, one question is arising more frequently: What will Arnold do?

Will he share the stage with Al Gore as a global environmental crusader, promote green technology for a Barack Obama administration, run for the U.S. Senate? Or might he pursue political reform on a broader scale, as he has hinted in appearances with New York City Mayor Michael Bloomberg, who shares Schwarzenegger’s independent streak?

Any of the options that would give him a larger platform undoubtedly would be more appealing than dealing with the gridlock inside California’s Capitol.

The partisan finger-wagging has kept him wrapped up in negotiations over faltering state finances for much of the last two years, and his approval ratings have followed the decline in California’s economic fortunes.

The 61-year-old Republican governor has been asked repeatedly whether he would entertain a position if offered one by the Democratic president-elect, most likely focused on alternative energy or other environmental initiatives.

He’s been coy in some of his answers, but has said he will remain in office until the end of his term in January 2011. He is not eligible to run again for governor.