MOD INPUT: Let's drop the political talk, ie the Birth Certificate stuff.
FWI, Obama's mother was a US citizen, so he is automatically a citizen by birth regardless of who his father was or where he was born. Even if another country declared him a citizen that does not invalidate US citizenship, so he could have a birth cert declaring him a citizen of somewhere else and still be good to go here. The US allows dual citizenship, which often occurs due to accidents of birth location. The law is clear on this, not really any room for debate.
Arnold was not born here, and was not born to a US parent so he cannot be a citizen by birth.