There's a phrase which would alienate an enormous swathe of class-conscious Britain. It left open the question of who could possibly be excluded if public education is for the "middle class". It took family members to translate for me.
The "middle class" is the 99%. The only people who aren't middle class, in current American political rhetoric at least, are the richest 1% of the population. Under the circumstances, it seems odd that there's still reason to use the word "class" with regards to distributions of Americans.