A government fork of bitcoin would do the same thing to bitcoin as the paper gold dollar did to gold, make it irrelevant, not used and valueless.
I get the analogy to gold vs. gold-backed dollars, but in Bitcoin's case I can't think of any specific changes the Feds could make to a fork that would allow it to both (a) obviate almost everyone's need for Bitcoin and (b) be enough different from Bitcoin for the government to be satisfied with it (and hardcore bitcoiners to be dissatisfied with it).
Well one change they could make is to declare the fork is legal, while the original is illegal with significant +10 years jail time for using it. This is not far-fetched, there is a clear historical precedent/blue print for them to follow. Gold had thousands of years of history as money and most of the public in 1913 only considered to gold to be money, yet by 1933 they were able to ban even simple possession. The force of government combined with the apathy of the people is the biggest threat there is.
For example, if the money supply remains un-changeable, this is awesome as the Federal Reserve has effectively been neutralized. If they make a fork that can be inflated, Bitcoin Classic retains its store-of-value properties and will be highly sought after. If they do something in between, we get a little of both. If they remove all anonymity possibilities in their fork, Bitcoin thrives in the black market; if they don't, awesome. If in between, a little of both.
Any fork could start out as an un-changeable supply. The FED's dollar was originally convertible to gold and thus had a fixed supply. Then during the next crisis they can default and fork again to increase the supply through default "for the common good". Again there is historical precedent for this. It took only 20 years for the FED to break a thousand years of gold history, how long would it take for bitcoin?
At one end of the spectrum they take just a few of Bitcoin's properties to build a system that is better than current fiat, which would be moderately liberty-promoting, while still leaving Bitcoin's differentiated value proposition very firmly intact. At the other end of the spectrum they adopt almost all of Bitcoin's properties, which would be extremely liberty-promoting, but leaving Bitcoin with little differentiated advantage. Either result is overall very good liberty-wise (though the result where they mimic Bitcoin quite closely may not be very good for Bitcoin investors - but that result is also highly unlikely), and I see no point in between those extremes that would be any worse. So I conclude there is nothing to worry about.
Any fork could start out benign at first, but turn downright 1984 Orwellian over time. The FED dollar was benign at first, it was considered the same as gold, and look where we are today.
I'm a believer in the bitcoin project and think it has a decent change of success. But it is not black or white where either bitcoin is guaranteed to fail or guaranteed to succeed, it is somewhere in between (gray).
All I am saying is making forks easy and common makes bitcoin's chance of success slightly grayer. We can argue about whether it makes is very slightly more gray or significantly more gray, but to me that doesn't matter, why make it grayer at all, no matter how much?