Is it possible?
You have to define what you mean by "shutdown". A shutdown can be a closure of a system, due to a fault or for maintenance. A shutdown can also be the act or process of ending the operations of a business/company permanently. In order for government to shutdown something, it must be controlled by an entity.
No one can shut it down,
but: They can damage it, by spreading FUD and they've already done it. It is pretty obvious that no government wants from its people financial freedom. An electronic currency that is decentralized wouldn't be liked from most governments. They know that they can't control it, so they try to scare their people to prevent its use. I think that in India it is still illegal to use bitcoin. A tech-guy, though, knows that making such thing illegal can't work practically. It is very hard to trace, especially if he/she's going through tor.
So no, governments can't shutdown Bitcoin, because they can't prevent the peer-to-peer sharing of the longest proof of work chain.