Impossible! If the gov copies bitcoin, it means they acknowledge bitcoin as an official currency co-existing with fiat. It will severely hurt the fiat's status. People may be dumping fiat to bitcoin, which will cause our financial system a bit chaos.
They'll somehow come up with a way to make their cryptocurrency more stable than Bitcoin, plus it will be backed by institutions and armies oficially and fully, this will allow for more stability. People is scared to death to put their fiat into Bitcoin and this is pretty much the only way to obtain Bitcoin. This is a big problem, and we are seeing it in the price.