President Obama... DO NOT BACKTRACK!!! You said that the Ground Zero Mosque was a local issue. This is exactly the right thing to say. You are absolutely correct on your Constitutional interpretation. It is very difficult to mess up "Congress shall make no law respecting an establishment of religion..." The federal debate ends there. It makes no difference if the Church of the Giant Phallus wants to erect a Holy Giant Phallus at ground zero. The Feds back off. They have zero power there.
The only government that has any authority over where a place of worship, or a religiously affiliated community center is placed in New York, New York is the County, City, and State of New York. If they deem that it is zoned correctly (it is) then all three have an obligation to step aside and allow the center, Mosque, or Giant Phallus to be built.
It is also the obligation of the city, county, state, and federal governments to make sure that those who choose to attend service at this religiously affiliated place are safe to do so. Not even if the proctor just says "Death to America" over and over again for hours. Not even if the secret passphrase to get in to the place is "Death to America."
Other religions have full access to this area. There is a Catholic Church in the same two block radius. There would be no fuss if a Lutheran group decided to put up a church in the same area. This is about demonizing a religion and branding the people who practice that religion as evil. Let's use a similar situation... Tim McVeigh was a Cristian. You better believe that he had religious motivations for blowing up the Federal Building in Oklahoma City. There are all kinds of Christian iconography all over the Murrah building site. Nobody has a problem. Double standards do not exist with Freedom. There is only right and wrong.
The First Amendment was written not to protect stuff that the majority likes. It was written to ensure that stuff the majority did NOT like could be expressed. This means that we let those that have differing opinions to ours say their piece. Even if we are fighting those that espouse those views. During every war we have ever had, sympathisers from every side have had their place. That is who we are.
Keep the faith Mr. President. For once you have the right idea. Build the building, and try to remember that your invisible man is no more powerful that the next guy's invisible man.