Mine was the same problem, and none of the replies gave any hints until yours.
I did dig up another thread where a Javascript conflict was mentioned, which let me find that my site template apparently has a Javascript conflict with VirtueMart.
When I changed in VirtueMart the template selection back to Protostar, then the U.S. State dropdown started working.
... I then got a 500 server error, probably because the Joomspirit template uses a different URL redirection scheme.
But now I just need to go shop for a VM-friendly template.