Most Americans are conservatives, if someone can communicate it properly.
Reagan managed to do it.
If you look at Reagan's CAMPAIGN in 1980, you do not see him beating the drum for pro-life, for "traditional family values," etc. Yes, he occasionally mentioned them, but his message was the economy and the Soviets, every time.
It all depends on how questions are phrased: if you say, do you favor complete unrestricted gun ownership, the vast majority of Americans say no. If you say, do you favor banning guns, the vast majority says no. If you say, do you favor drilling? Most Americans say yes. If you say Do you favor drilling even if it means some environmental damage (and I'M NOT SAYING THIS IS WHAT HAPPENS, ONLY HOW PEOPLE CHANGE THEIR RESPONSES IF YOU ADD IN QUALIFIERS, AS THE DEMS WILL DO), the answer is overwhelmingly mixed.
What Reagan did was campaign on consistency. Everything tied together---opposition of the Soviets was both for national security and because of their "godlessness" and anti-life culture. So I disagree that you'd get a huge majority of Americans to support "conservative" principles no matter how they are communicated. You can get a committed MINORITY to persuade a working MAJORITY on pragmatic and practical grounds ("This will be good for your wallet . . .")