I'm not an American citizen, however...
I would support this move. I do not think it violates the first amendment, as much of the basis for the law/social values and core principles in the United States (and many other western countries for that matter) is based on the Ten Commandments. So if these values/laws are allowed, then why not a Ten Commandments Day? Why not take a day in the year to look back to our roots? Might get some skeptics thinking.
About the National Day of Prayer....I'm also supporting it. However I know little details about what religions it's aimed at.