One of the things that makes America great and/or terrible is that you can basically sue anyone for anything. If you can find a lawyer who will sign off on it, you can pretty much sue anyone at any time.
Republicans in Congress, led by John Boehner even did so a couple years ago. According to PolitiFact (which I highly recommend in general), this is the only time a sitting President has ever been sued by Congress.
Of course, suing someone and suing someone successfully are very different things. The lawsuit was immediately thrown out and nothing came of it. Many people mocked it as nothing more than a political stunt.
Still, there doesn't appear to be anything in the Constitution saying that Congress can't sue the President, or even potentially win and make him pay damages; it's just that this has only been tried once and didn't work.