Do you have any idea how Marxist that sounds?
There is probably not a single major corporation that pays any of its employees minimum wage. A rise in minimum wage will not hurt big corporations. If anything it will benefit them. The guy who will get hurt is the mom and pop company and the employees of the mom and pop companies. When the mom and pop companies are all forced out of business then the big corporations will move in to fill in the gap.
Do I care?
Their corporate existence is a privilege extended by the state, created as an act of the state. The state has every right to demand corporations fulfill certain responsibilities in return for their franchise.
It's not Marxism to believe in corporate responsibility. Marxism disbelieves in personal property. It is not inconsistant with capitalism to believe that corporations owe certain duties to their employees. In fact, my measures are intended to keep capitalism alive and forestall a Marxist-style revolution. Keep abusing workers, however, and you see a proletariat revolt. Marx was right about that; his error was in believing this would be a good thing resulting in an utopian society. It will not; it will result in the oppression you saw in the Soviet Union.