The Guardian profiles Arnie - sometime bodybuilder, actor and now Californian governor. There's a career path already trodden by others - Jesse Ventura was a governor after a career in wrestling and Ronald Reagan made it all the way to the top job. It is clear that Arnie has similar ambitions, but his birth gets in the way.
Unfortunately, the US Constitution (Article 2, section i) requires that the President be a natural-born American and Arnie is Austrian by birth, although he became a naturalised American in 1983. It may be that most elected jobs in the US are open to all Americans, naturalised and born, so to keep the Presidency solely for 'real' Americans is a little anomalous.
Changing the Constitution isn't an easy task, though. The prime method is by passing a two-thirds majority in each house and then must be approved by three-quarters of the states. This can be quick - amendment guaranteeing the vote to everyone over 18 cleared the hurdles and was ratified in 100 days - so it can be done. However, the process is not meant to be easy and more than 100 amendments are proposed in each session of Congress. 27 have been passed in more than 200 years and ten of those form the Bill of Rights, passed only 2 years after the Constitution was written.
In fact, the amendment that Arnie seeks has already been placed before Congress - and will be again, no doubt. Getting it past Congress and three quarters of the states may prove more difficult, especially as the Democrats would know that it was only being passed to allow Arnie a tilt at the main job.