Minimum wage is illegal? Take it it to SCOTUS.
I believe the government lawbreaking reference was to illegal immigration.
Obviously, the SCOTUS would uphold it.
Then again, they legalized abortion too. The US Supreme Court has very little to do with natural rights anymore, or with the Constitution itself for that matter.
I think, though, that the founders would absolutely have been opposed to the government setting prices and wages between private citizens. In fact, the concept was likely so alien to them that I doubt it ever occurred to them that there would ever be such thing as federally fixed wages and prices.
Had they been able to imagine such a thing, I'm sure they would have explicitly denied the power to do such a thing.