Faithful (and generally adversarial) commenter James Elliott has claimed the problem with conservative nominees to the Supreme Court will have to do with their adherence to the Constitution in Exile. I had not heard the term before, perhaps because I followed up law school with a lot of study of religion, so I went looking.
Pioneering legal blog The Volokh Conspiracy has an excellent post by Randy Barnett (a significant legal scholar) all about the Constitution in Exile and whether or not it's a load of crap. You'll have to read to find out.
Hint: There's a good chance that it's cr_p.