Reagan and Thatcher both denied the role of government by decrying its "inefficiency" and claiming the benefits to be had from the efficiency of the free market. The only way this can be argued is by convincing people that "they" paid for the benefits from their governments via their taxes.
Thatcher even stated such directly when she claimed "There is no "public money". There is only taxpayer money". Reagan alluded to this more than making such direct statements, but the gist was the same. Those paying taxes were supporting lazy and criminal "others". He even went so far as to concoct a totally false example of people (who he insinuated to be primarily black women) who were driving new luxury cars and paying for their groceries with food stamps.
If one assumed that their tax dollars actually were going to support sloth with more comfortable lifestyles than the ones paying taxes enjoyed, or that such money was misdirected away from employers and causing them to hire fewer workers it would be natural to become angry, and anger is the currency the GOP functions with to this day. Trump is just a less refined version of Reagan, but that matches up well with the devolved GOP base.
The private sector "is" more efficient at most things than government, but not so much so to justify the net cost increase from "free" to footing the whole cost and financing it to boot. What the (federal) government does extremely efficiently is "pay for" things. This is because it is the sole source of the US dollar in the economy and never needs its own dollars back to enable its spending. Our taxes serve several important functions, but none of those are "funding" our government at the federal level.