A few months ago, America started to limit visa-free entries by Hungarians. It's long been concerned about the somewhat willy-nilly way Hungarian passports have been handed out under Simplified Naturalization.
The details aren't too relevant here -- they're in the link below -- but what is relevant here is whether Hungary might impose any reciprocal limits on Americans.
Have there been any suggestions that it might?
(This of course comes on the heels of the US cancelling its tax treaty with Hungary.)