The joke is that in the Simpsons universe, Swartzenegger is a completely different guy who just happens to look and sound exactly like McBain, and also he's had a very similar film career.
The reason they used him is because they didn't want to date the movie by using Bush.
John "America" McC/Bain: The American president of America that Americans who live in America have being America-ing for in America since America Americaed its first America. America.