Your problem is thinking that Dems and GOP are real things. There is establishment...that is all.
There is definitely a divide between how Democrats and Republicans govern. They come together on many issues, but that is often for the best. You make Americans coming together on something we can agree on sound bad when you say "establishment." It is often very good.
The fact is that Democrats have increased minimum wage, and will almost certainly figure out a way to increase minimum wage again. Meanwhile, Republicans have fought minimum wage increases tooth and nail, and will continue to.