They can not do anything, but politely ask bitcoin bookies not to accept US players.
They can also start blocking websites.
Another thing is that they can try to make bitcoin illegal, which is not possible to enforce.
What is possible is insanely strict regulation of Bitcoin exchanges like in NY. But we are talking about years here and there will be always a possibility to echange USD to BTC and vice versa, if bitcoin is needed. For sure even if the battle will progress to this stage, the money movement will be easier than gamble-dollars nowadays.
If you talk to God, you are praying; If God talks to you, you have schizophrenia.