I oppose both illegal immigration and minimum wage. While they can both impact supply and demand in a labor market, they are separate issues for the following reasons:
1. Minimum wage is a price floor that locks low-performing domestic workers out of work. It is the main driver of the rampant homelessness, drug use, and vagrancy that is wrecking many American cities. It says "if this person can't generate you X per hour (plus payroll tax and insurance) then don't hire him." And so many folks simply can't generate that much value so they go unemployed, accept handouts. and many use drugs, which are generally permitted or tacitly permitted in high-minimum-wage markets.
2. Illegal immigration creates arbitrage so that workers from lower wage markets can enter and undercut domestic workers so long as they keep their living costs low. This is the same phenomenon seen on oil rigs, shale towns, and gold strikes. Business owners love it, workers like it, but very little of the money stays local. It is not a recipe for a stable economy or a stable society.
In the long run employers, employees, retirees, and children are all in the same boat and would do well to build a ladder with rungs at every height and with incentives to keep all of the work and all of the money local.