Those who have been elected to either Congress or a statewide office. The same credentials that Ron Paul has or more, more than Alan Keyes or Hugh Cort. BTW, John Cox dropped out in December-- not that anyone noticed.
That's sounds like a reasonable standard, but it would exclude Giuliani. It also would have excluded Dwight Eisenhower in 1952.
My main point, though, is that there has to be a line somewhere; once that's accepted it becomes a matter of where to draw it. But the concept of having a standard is clearly valid.