Immigration, the Nanny State and Unintended Consequences

It was about a week ago that I was driving home from work, listening to talk radio as is my habit, when I overheard a host talking about how the American Welfare State was an incentive to illegal immigration. I don't know that people come to the US to take advantage of our welfare system. I tend to believe that most people come to the United States looking for work. And let's face it, work is here to be had. Employers, especially in the agricultural sector, often contend that the reason they need to hire immigrants is that American workers are unwilling to do the work - of course, they always seem to leave a very important phrase off of this statement, "at the wages they offer." And that is when it dawned on me. The American Welfare State may, indeed, be an incentive to immigrants - not because they come for the benefits, but because it gives American workers an incentive not to work.
Why should a person do the back-breaking work of picking strawberries when they can exist - maybe not well, but exist nonetheless - on the government dole. Even if a worker could make more cleaning hotel toilets, how much more would they need to be compensated before they chose to do that instead of being paid for doing nothing at all? The Welfare State may actually be artificially raising what workers perceive to be a "living wage", while at the same time enticing immigrants and employers to find common ground in the underground economy.
I was unemployed recently, for approximately three months. I was able to make ends meet during that time by selling the small portfolio of stock I had accumulated, spending the minimal severance package I received, my tax refund, and unemployment. I doubt that I could have lasted much longer without starting to skip payments on credit cards, my mortgage, etc. I was picky, though, in my job search. I confined it companies in my immediate area, not desiring to have to make a long commute which would take time away from my family. That being said, as my funds ran short, and I started to experience shortfalls, I would have lowered my expectations, made compromises, and ultimately done whatever I had to do to support my family and pay my bills. I don't think that other people are any different. We will do what it takes to survive, but if we can survive before "going to the mattresses" we are likely to make trade-offs.