Very possible but that currency won't be bitcoin, the federal government are cooking up something that'll most likely cause an uproar in the community. They'll bring in a currency that would be a cryptocurrency but won't be a decentralized one instead it'll be operated by centralized bodies.
Facebook wanted to do something similar but didn't get an approval from the fed because they know the advantage would be in favor of Facebook as the first mover if they were to grant their request.