The Right’s narrative on this is screwed up.
It’s not “jobs will be lost because employment costs will be too high”.
It’s “government prohibits producing less than $15/hr in value”, to wit “it’s illegal to work if you’re not productive enough”.
This is just a new twist on the ancient “debtor’s prison” concept: if you don’t earn/own enough, you’re not allowed to earn anything - you exist only at the pleasure & expense of the State.
You are right, but vast numbers of the population when using that terminology to explin a $15.00 wage would be looking back at you with a blank stare...
Just tell them their Big Mac will be $8.00 now and the light will bulb come on...