Shall I go ahead and start the over/under pool on how long it would take before it was hacked? I think it's a compelling idea, but it would probably be the most-interesting target in the world.
Depends on how it's implemented. As always, the devil's in the details. If it were properly sandboxed, it seems it shouldn't require anything more than the government's unique ID eg a Social Security Number as a backing for tokens granted. In that regard it wouldn't be any more juicy than any other common store of SSNs, of which there are sadly quite a few.
You would presumably be able to use this information to de-anonymize previously created tokens, but that would require you to gain access to the token as used, which would also require a breach of Twitter or whoever else. It's not unthinkable, but if Twitter is breached you might have enough info to de-anonymize its users anyway.