Personally, I think there would be a public "Get those unnatural SOBs" and private "Psss - want to live a good life as government employee" message going out.
That there would be some elements of most governments who want the supes on their side... Imagine a BC Vampire looking into someone's eyes and saying "Tell the investigators everything you know" - what interrogator wouldn't want that? Or a Fae assassin working for them. Or a wizard that they can control. Or a ...
Yes, they would want some supes working for them.
There's a nice short story along those lines that's legally available online. Called
"A Colder War" (At
http://www.infinityplus.co.uk/stories/colderwar.htm ) it mixes real world history (up the Regan years) with the Cthuhlu mythos - showing what goes on behind the "Of course we don't work with dark forces" facades.
Richard