Interesting question. I’m more inclined to say, “Yes, it should be,” than “No,” but that’s assuming that “impeachable offense” means anything.
Thing is, that First Ladies have no business having an agenda that requires the President’s signature. Women in America have the ability to do their own thing without permission of a man and frankly Michelle’s lunch program antics have done nothing but damage. Why can’t First Ladies concentrate on fashion (like Jackie O. did) or being a good hostess or simply making life better for the President? Cripes, there are a lot of things a First Lady can do without meddling in politics.