Trump should issue the following statement, “Background checks are a smart qualifier. How can we be sure that those who are charged with writing and administrating our laws are responsible without full and accurate and published background checks? How can we be assured that those who are responsible for overseeing and reporting on our elected officials are capable and true without full and accurate and published background checks? When I become president, every elected official and every employee of every agency, and every reporter in every newsroom, will be subjected to complete background checks. All results will be published - completely. Anything less would be unfair and irresponsible.”
I’m pretty sure there would be some big Fourth and Fifth Amendment issues there. But it does make a good threat.