I don't know specifically about the story Partha mentioned, but Ddrak linked to one of the articles I've read on the subject. Here's another.
And yes, illegal immigrants are purchasing goods and services in the US. They need food to survive. They need shelter to survive. Yes, money gets sent back to Mexico. Money would still be going to Mexico if they were legal guest workers under the model you've previously proposed (And I agree with, I'll add), so I'm failing to see the issue you have with that.
Even if the studies citing illegal immigrants bolstering our economy are wrong, we'd still be looking at a prohibitively expensive undertaking in kicking them all out. We would need to hire tens of thousands of new INS employees, and is that something we really want to be doing at this juncture? Beyond that, you've admitted we need them for farm labor if nothing else, and the article Ddrak linked reinforced that.
So, many of our crops would die in the fields, or the price of these goods will skyrocket. Inflated food prices are another thing American's don't want to deal with (And many of us simply can't take on) right now. We'd either see an explosion in EBT claims, or the impoverished class will just starve out.A crackdown in illegal immigration in 2004 caused a shortage of workers needed to bring in the lettuce crop in the Western United States, said Powell, which he said caused a $1 billion loss for the industry as many growers had to leave their fields unharvested.
"To hire Americans to do it, they would have had to raise wages so far, it wouldn't have been worth it for them," said Powell at the Independent Institute. "It caused less of a loss to leave the crop to rot."
I'm all for finding a reasonable solution, and I think you've got it with the guest worker program. But for now, as we've all noticed, neither party truly wants to do anything about it.