For the government it would be perfect to have an economy that only runs on a digital currency, as long as the state has the monopoly and full control over the money supply of that digital currency.
You can transfer value in any number of ways besides your country's sovereign currency. People trade stocks, they trade items on eBay, they trade jewelry, etc. Every business contract is essentially a trade of value.
There's no way any government could have a "monopoly" over this. (And Bitcoin is just one more means of trading among thousand of other ways).
And Bitcoin wouldn't change a government's ability to run deficits (?)...