Whatever one thinks of the President's actions so far, it does not seem likely that there will be a majority in Congress in the near future to force the withdrawal of U.S. military forces. But there might well be a majority in the near future to insist that a military campaign that goes on for months needs explicit Congressional authorization.
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.