More diligent enforcement of the labor laws would, in fact, result in a defacto increase in the effective minimum wage. To the extent that those desperate enough to accept subminimum wage are illegal immigrants, enforcing the minimum wage would also have a beneficial effect on the problem of illegal immigration. Basically it accomplishes the same thing as what I outlined.
What does it tell you that fifteen states find it necessary to set a minimum wage higher than the Federal standard? In a large part of the country, the Federal minimum wage isn't a livable wage, which is a pretty good sign that the Federal minimum is too low (and likely inadequate in many more than the fifteen states willing to address the problem). Or it needs to become more discriminate, and take into account local costs of living.
Block off the southern border, either by personnel or barriers or both. Once the inflow is dealt with, we can start worrying about those already here.
You RightWingers, you think that every problem can be solved with military force. How much would it cost to build Fortress America? I mean something that would actually work and accomplish more than giving RightWingers a warm-and-fuzzy illusion that we're Doing Something? We'd have to seal off every inch of our entire border, not just the part that abuts Mexico. Remember that the Germans just went around the end of the Maginot Line, and in any case illegal immigrants come in from all directions, not just from the south. Only a closed fence would do the job, enclosing 100% of America's borders. It's a problem in three dimensions, from the ground on up to space, and down into the oceans off our shores--we're talking about englobing a volume of territory and sealing it off so tightly that nothing bigger than a jackrabbit could sneak in. We're talking about trillions of dollars to make it work. How about we just put the poorest quarter of Mexico on welfare and pay them to stay home?
I'll bet you're itching to retort "well then how would you solve the problem?" Unfortunately, Tom, my message is that some problems don't have an easy solution. That's what you're going for with this dream of just walling-off our souther borders so that the problem of illegal immigration will vanish overnight. But it won't work, and attempting it will make us worse off than before.
Those poor Mexicans aren't enemy soldiers we can morally shoot on sight. We can only make them stop heading north if we remove their incentive, either by reducing the odds of finding low-wage work here (the more coldhearted solution), or by improving conditions there (the more humane solution). They're just humans trying to survive, and their actions can only be changed by changing the parameters of their survival equation.