You could probably impeach Obama over drone strikes if nothing else since those are technically acts of war/aggression violating a county's sovereignty. Addendum: The articles of impeachment for Bush that were introduced into the House that never went anywhere – there's fourteen of them – http://en.wikipedia.org/wiki/Efforts_to_impeach_George_W._Bush – it is pretty depressing that probably every modern president has committed impeachable offenses or war crimes. It's almost as if that's accepted policy. Almost.
When fringe figures like Rep. Kerry Bentivolio (R-Mich.) talk about impeaching President Obama without cause- it's a mild curiosity. When U.S. senators push the same idea- it's more alarming.