It doesn't really matter what the public thinks because people have different views on things so can't take an opinion without analysing the situation based on someone else's opinion.
I believe your answer is the Aztecs.
States because the American people wanted to prevent the central government from becoming tyrannical. But the central government was too weak and could not rely on the states for support.
Impeachment is a long process and lots of times doesn't work in time. This happened with Bill Clinton. He was on trial to be impeached but finished his term before he could be removed from office.