Ignoring the Constitution is an impeachable offense. Failing to submit a budget, drone strikes on American citizens without due process, selling firearms to criminals intentionally which were then used to kill Federal Border Patrol Officers ("Fast and Furious"), diverting financial assets to campaign contributors, failing to protect our embassy staff abroad (Benghazi), failing to obtain Congressional approval to go to war (Libya), denying First Amendment rights to conscientious objectors... The list goes on and on.
There is plenty of evidence to support impeachment. The bigger question is whether or not the Republicans have the moxy to impeach Obama knowing that there is no way the Senate will convict.