I also agree with that he was not saying that the Muslims building a mosque there was a "smart" decision -- “I was not commenting and I will not comment on the wisdom of making the decision to put a mosque there. I was commenting very specifically on the right people have that dates back to our founding."
I think the Muslim group is being politically/socially insensitive to build a mosque there (given that feelings -- right or wrongly run high about that ground)... but that they do have the right to (so long as they obey all the zoning laws, get the permits, etc).
I'm not sure how I feel about the National Day of Prayer thing. The National Day of Prayer is not a holy day/month observed by a specific religion -- like Ramadan, or Passover, or Easter or whatever. President George W Bush was the only one to hold observances at the White House -- even President Reagan who got it going (President Truman signed it into law in 1952, but it was largely ignored until the 80s) didn't have anything at the White House.
It is an interfaith day of prayer supposedly, so I don't see what the harm would be in having a ceremony at the White House. Reportedly, Thomas Jefferson was the first to host an iftar dinner and it is a custom of modern White House dinners -- as they do host seder dinners, Christmas dinners, and other religious dinners. Personally, I don't think any "religious" dinners -- regardless of the religion -- should be held at the White House as a public event. Separation of church and state and all that. If the president wants an Easter dinner, for example, he should have one in the private quarters as private meal for his family and friends.
If he or she (whoever the president is in the future) wants to attend an iftar or seder, it seems to me it should be at a mosque or synagogue -- a religious place for a religious ceremony. The same would be true of National Day of Prayer event -- go to the National Cathedral or neutral ground like Nationals Park (the baseball field) or some such place.
Perhaps I'm just a cranky old Quaker (okay, so I am a cranky old Quaker), but state involvement in religion has long been bothersome to me. Almost 400 years ago, the state (both England and some colonial governments) had no problem locking up, exiling, and even hanging people for being Quakers. They said where we could meet and where Meetinghouses could (or could not) be located. I had hoped we had moved past that... but evidently Bob Dylan was wrong. The times, they are not a-changin.'