Can you qualify that question? I never heard that president Obama suddenly works for a construction business.
But seriously, the mosque in New York will be build by a construction team paid by Muslims. Muslims applied to build this mosque and the city of New York allowed it to them. If the city of New York wouldn´t have wanted it, they wouldn´t have allowed it. Very simple.
Presidents do not sign such kind of allowances.
So why do you think that President Obama has anything to do with the building of a mosque?
Certainly also in other cities there will be religious communities building synagogues, mosques and churches, but all such things do not belong to the job of an US President.