I don't think it's that government is ungovernable, but that we've accepted rhetorical flourish as truth -- in this case Reagan's "Government isn't the solution; it's the problem." Or something similar.
Government is neither. It is neither the solution nor the problem, but good government is essential to a well functioning society or country, and good government is philosophy neutral. The regulation undertaken by government or government direction is no different. Regulation can be bad, or it can be good, there can be too much or too little, but regulation itself is neither bad nor good, and if there's too little or too much it's because we've made it that way.
The same goes for government, if government is bad it's because we've made it so, and if we don't believe in the ability of government to be functional it won't be. It's a catch-22: government hasn't delivered so we don't believe in it, and we don't believe in government therefore it can't deliver. This goes for both parties in the United States, and I'm not convinced the current president believes in the ability of government to deliver -- actually I'm not convinced he believes in much other than his ability to give a good speech.
But good governance is neither a property of either the right or the left -- the Scandanavian countries have demonstrated that under certain conditions leftist philosophy can produce good governance, but then places like Singapore, Korea and Taiwan have demonstrated that rightest or even military dictatorships can produce good governance, and prosperous socities. On the other hand there are places like Argentina and Italy where poor governance by both the right and left has proven ineffectual in solving the problems faced by such countries despite the natural resources and human talent or the educational advantages these countries have or may once have had.