First would you really want to look at Bush (or Clinton) for 6 years before you have a chance to throw them out of office?
Second, the President is automatically a lame duck. There is no reason for Congress to cooperate with the President at all. They can send him the most extreme legislation that can pass Congress just for political purposes.
Third, without a reelection campaign voters have no way to tell the President what kind of job he's doing. Yes there are the congressional elections, but the President isn't going to care about getting reelected so he won't be listening to the voters. He'll keep demanding the same stupid legislation that voters rejected in the midterm elections.
Overall it reduces the President's accountability to the voters and does not encourage Congress to pass responsible legislation. If the proposal reduced the term to 3 years with a max of 2 terms, I think that would be a better idea.
A three year term is a bad idea. You would spend half your presidency campaigning to be re-elected. I like two six year terms. The Confederacy had a 6 year presidency.