Nope. I very doubt government will want to relinquish control...
As a sub currency it could gain mainstream use but i think there will be much blood before BTC replace the Dollar.
Modern governments seem very infavor of relinquishing control. That's what this whole globalization thing is about. Most governments want to surrender to a one world government. So if a one-world-government is not far-fetched then neither is a one-world currency. Although I do not think this currency is going to be bitcoin, nobody wants those ridiculous fees.