I support the idea of a minimum wage. It is the scaffolding on which self-sustaining arch of fair wages is built. But that does not mean that any particular level can be too high, so the process of raising the the minimum wage becomes something like a trial, in which the burden of proof is on those who want to raise the number.
Certainly, there is a number (in today's dollars) that would be unsupportable. Given the tendency of the people to vote themselves largesse out of any fisc they can find, there needs to be push-back against increases in the minimum wage.
Over time, the number should be matched to the marginal cost of meeting the demand that wider distribution of purchasing power will engender. That's a matter of technology, because, ironically, the more workers are replaced by machines, the more the remaining workers can be paid.
All of this points toward the coming UBI, a better "minimum wage" that effectively rewards the investment we all make in being good citizens of a stable and prosperous nation, and at the same time helps us to remain such.