If he did, what possible effect would that have on his ability to govern the country? I am much more concerned about Obama's religious beliefs to the extent they are represented by Rev. Wright (i.e., Marxist racist liberation theology), since they could seriously impact the polity of the country, than about Romney's Mormonism, so long as he is not pushing legalization of polygamy (which the current Mormon church does not support anyway).
Used to be if a presidential candidate told you that he was going to become a God and rule over his own planet of worshipers, and you could see that he meant it, it was a deal killer.
Your follow-up Q: If he did, what possible effect would that have on his ability to govern the country?
It boils down to (a) character and (b) discernment.
If a man is so deluded about his own identity, and flunks THE MOST basic discernment about himself as well as other major blocks of voters (Another example, Lds theology teaches Christians are "apostates"), then we know that gullibility to deception doesn't end there.
If a POTUS flunks basic religious discernment in foreign policy issues, like anything to do with Islam, that could readily spell unnecessary problems developing.
But -- worst of all -- we know that in these times crisis after crisis can hit the world and the US. THE BEST resource a POTUS has is the eternal resources of THE sovereign god. No president ever "rules" apart from a sovereign lord, who rules the world. If the POTUS is praying to an unknown "god" -- somebody who got the "god job" as a man...especially in a crisis situation...why would THE true God respond to that?
Just think of a scenario of the TV program "24" where they had the "president" on that show dealing with terrorist threats, etc...I'm sorry, but one of THE problems with the Democrats -- and it probably was shown most acutely in the immediate aftermath of the New Orleans area hurricane -- is that their "savior" and their "security" stops at the govt & Supreme Court.
With a president who embraces a "I am god" mentality, we get the same "ceiling."
The "character" issues that also intersects here is a POTUS who thinks he is divine = the most tremendous pride, arrogance, and hubris possible. It is no "anathema" to THE God -- that the prophet Isaiah indicates this was THE ORIGINAL SIN in heaven that got the angel, Lucifer permanently booted and led to the expulsion of up to 1/3rd of angels who joined the mutiny ... (you can read that in Isaiah 14...I think around verses 13-16)