Yes, there is a perfectly legal way to replace Barack Obama with a more competent leader.
Step 1.) Gain a clear majority of the House and a two thirds VOTING majority of the Senate. (The Senate majority need not be of the same political party, just of the same political mind.)
Step 2.) Impeach the President and the Vice President.
Step 3.) Swear in the Speaker of the House as the new President.
While gaining a majority of the House appears possible if not likely this year – it would take a major catastrophe to gain a voting majority in the Senate. However, catastrophes happen.