No, they can't replace Obama very easilly. The best they could do would be to (1) impeach him which means to accuse him of a crime and then (2) convict him of that crime. #1 is fairly easy, but #2 is very difficult.
Having a republican congress and a democrat president is probably the best combination that we've ever had. The 1990s were fantastic in large part because of that combination. The president can still do a lot in the way of a veto. The republicans won't get anything they want unless they compromise and give the president what he wants. In a way, that is even easier for Obama to get his way with republicans in control of congress than with democrats in control. Democrats have a habit of bickering, delay, and watering down their bills when they are in control of congress. Suddenly if republicans are in control, then there is only one democrat (Obama) who gets to control what needs to be in the bills for the republicans to get their way.