"An influential group of conservative intellectuals believes that American liberal democracy is illegitimate.

That's because it's the only position conservatives have left. Their political arguments have failed in our democracy because the majority aren't interested in them. Attacking the system is the only strategy left to them. Conservative legislators damage our system daily through Congressional gridlock, with which they hope to convince voters that the system doesn't work well enough to keep. 

They misuse government for partisan purposes, like faux investigative committees, and time diverting measures like fifty formal votes to repeal or de-fund Obamacare instead of dealing with the problems of the country. They make sure that the people's business does not get done because they have to attend to a more important agenda - wrecking the people's government so they may fashion a new one nearer to their heart's desire. Authoritarianism? It fits them like a glove on a fist.