I would like to believe(perhaps naively) that the segment of population which genuinely believes in doing away with democracy is pretty small.
However, in case such an event comes to pass, what is far more important is the segment which actively opposes such a power grab. Authoritarians reply on the passiveness of the majority coupled with a small but very vocal and rabid fan base.
It's quite possible that a slow and gradual slide in that direction is underway, but the minute even a small faction of people actively oppose that, strongmen tend to find the limits of their power pretty quickly and mostly in ways that are pretty detrimental to their health.
The civil rights movement is a pretty good example of the power of a small set of people being enough to have critical mass.
The civil rights movement would not have succeeded without the confluence of growing anti-government sentiment and protests around the Vietnam War, and fears about the spread of communist influence in the US. This forced American leaders to give 15% of their population basic human rights denied to them under Jim Crow laws.