That is completely false. We put a man on the moon in the 60's. Now NASA is a shadow of its former self. U.S. funded computer research programs gave birth to the internet, as well as many other inventions. Now it is almost impossible to get government research funding. Republicans have dialed back regulations for decades, and whenever they can't dial back regulations they massively cut the funding for said regulators. I'll post links and examples later today when I get the freetime.
Certainly there are some areas where government spends less than they used to. But, in inflation adjusted dollars, and in the very visible ways in which it touches one's life, government in the US is much, much larger than it has ever been. In the areas of education and healthcare (which you mentioned specifically) the increase in cost directly coincides with the increase in government involvement in those sectors.
I've spent a very large chunk of my adult life trying to shrink government, and losing most battles - especially in healthcare and education. You can post whatever links you want, but my statement is an objective fact. No amount of links is going to change that. You could argue (incorrectly, IMO) that government involvement was in response to, not the cause of, the increasing costs. But, you cannot reasonably argue that the two have not increased in tandem, or that government is more involved in those (and many other) sectors than it ever has been. Government just is much, much bigger than it ever has been.