Yes, it's called an Impeachment. According to the Constitution it can only be for an high crimes and misdemeanors. The Congress then holds a trial and if convicted the President is removed from office. Then the next in succession becomes President until the next election. Basically, it's not going to happen over this. Remember, Congress agrees with the actions of the government more or less.

To more directly answer your question. There is no popular recall mechanism. The closest would be if there was enough public outcry to their congressional representatives that Congress began to move against the President. The bar is really, really high on this. It's not going to happen.