Typically I distrust analogies like the one you presented, but as analogies go, that’s pretty good.
I would counter that the slogans adopted by a “base” are:
A)A short hand for broad and more complex ideas that aren’t always perfectly understood by even the base, i.e. “workers of the world unite!” or “dyslexics of the world untie!”
B)there is some other broad idea or demographic that unites a base other than slogans.
I would argue that the base [by its definition as a mass phenomenon] is not capable of understanding anything beyond the level of slogans. Thus whatever unites it, has to be either slogan-primitive, or primitivizable to the level of a slogan [for example, "demographic ideas" are perceived at "us vs. them" level - try to make it more "basic" [pun intended] and slogan-like!]. Now, how many correct conservative ideas are driveable to such level? - not many, beyond national security and low taxation. One could include "limited government" in its slogan form "ef off and leave me alone!"