He has only one real power that no one else can take away: the power to bring bills to the floor.

That means McConnell can block any and all of Obama’s appointments, both executive and judicial. And that is what McConnell should threaten to do if Obama attempts to carry out executive amnesty. It is a threat that is directly related to the powers that Obama proposes to abuse, and it is better than threatening to defund the government or even particular agencies, which would have the disadvantage of punishing innocent individuals.
If Obama persists, then defunding is on the table–but it should remain targeted. And it should aim directly at the White House itself, cutting funding for all positions necessary to carrying out the president’s non-security powers, even grounding Air Force One if necessary. 

McConnell should be prepared, ultimately, to defund the White House–even while passing the rest of the legislation that he and Boehner have on their long to-do list.