It's ridiculous that this is an issue. Of course Obama is going to allow it-he has zero grounds on which not to. Muslims have the same freedom of religion as Christians.
IMO, the Islamaphobia in the US is appalling. The actions of extremists do not bear on the religion as a whole.....unless we want to declare Christians as being clinic bombers, prejudiced murderers, and spreaders of incurable endemic.
Yes, they could change the zoning to create a radius in which no place of worship would be able to be, but you can't single out the Muslims. However, I doubt the people getting all upset would like that, as it would probably mean a few Christian churches would have to move.
On a practical standpoint, given the rampant Islamaphobia, building a mosque that close to Ground Zero might be a bad idea as it could inspire the paranoid to do something stupid.