There were no overt threats to use nuclear weapons in Vietnam, but it was definitely part of the leitmotif of the day. I have written a bit about this here.

The US only used explicit "nuclear blackmail" with non-nuclear countries a few times. Nukes were talked about by government figures publicly as a possibility in the Korean War (but it was a bluff), and they were explicitly threatened against China in the Taiwan Strait Crisis (which did cause China to back off, but also to invest in their own nuclear program). They were somewhat loosely threatened in the Gulf War, as well (which is an interesting case, since there is evidence that Saddam thought the US would use nuclear weapons, but did the unwanted things anyway — he was "undeterred" in a sense).