The Republicans believe that suing Obama will excite and turn out their base voters, and they're betting that this benefit will be larger than any political blowback. Whether they're right in this political calculation or not remains to be seen. But what is undeniable is that, so far, this lawsuit is nothing short of laughable.
Americans should be protected from interference with their faith as well as attempts by others to impose their beliefs. The institutions of government and church should be kept far apart, while the political realm is left open to arguments of all sorts, whether based on theism, humanism, or something else.