They would likely decline. Why would they give him publicity? They could simply say they had other campaign priorities and commitments.
After Thompson skipped the NH debate by waiting a day to announce on the Tonite Show, he would have little room to complain.
None should fear it, and it would certainly give Republicans/Conservatives/Independents and even Democrats a much needed SERIOUS airing of issues.
Imagine real debates, one on one. How refreshing. They are all capable men, each would do fine. And their differences would be interesting.
AND I would bet it would put the GOP ahead in even generic polling, and give us a boost against the Dim Congress and the DNC candidates for President.