There are plenty of stories circulating about the dollar coins that were minted without the catchy "In God We Trust." For example this one http://seattletimes.nwsource.com/html/nationworld/2003605634_webdollar07.html. It appears the one-dollar coins are selling for around $50.
Now, I'm not trying to make any kind of agnostic claims about the worth of the slogan, but it appears to me that we might be sitting on a solution to the defecit. All we need is a good eraser.