If the households and businesses that hire illegal immigrants do so in order to save the cost of paying taxes, and they will not pay the taxes even when an employment agency handles all of the paperwork for them, then what we have is more than an immigration problem -- we have a tax rebellion.
As long as we have the safety net and the minimum wage, Americans will not want to work for the wages offered illegal immigrants -- and legally could not do so even if they wanted to. So my solution to our immigration problem would be, not "immigration reform," but economic reform. I would implement fundamental structural changes to our economy, such as abolishing the minimum wage and the welfare state. Soon enough, the jobs currently being filled by illegals would be filled by Americans. Illegal immigration would not appear so necessary to our economy, and perhaps we could muster the political will to enforce our immigration laws.
...if we legalize the illegals, then once again, there will be an economic need for people who are willing to do the unskilled jobs for a pittance. And the cycle will continue. It happened after the 1986 amnesty, and it will happen again.
For Discussion. To what extent is the "illegal immigration" problem really a black market in labor?