I believe the point he is trying to get across is that because a lot of illegals are paid under the table, there isn't a sufficient way to try to tax them. Which is true, but that is a byproduct of the larger issue, the employer trying to save himself a few profit points by hiring, and paying them in the first place. Blame is being squarely placed at the wrong feet here. Most of these people just want to work, they have no roots in this country, no reason to care whether or not Joe 12-pack (do not say the other name) is upset about him working illegally, because he is just going to go back to Mexico and live it up for half the year laughing all the way to the bank.
Don't get me wrong, I'm all for reform up and down regarding immigration, particularly regarding access to welfare, or healthcare. However being a product of immigration (first generation Chinese) I have a personal understanding of how the US was looked upon as a beacon of hope for the world, a place where your dreams can come true. To most immigrants that dream is simply being able to provide for their families, in relative safety. Its hard to fault people for wanting to do that, if the roles were reversed you would very likely do the same. The issue isn't punishing people for wanting to work though, its about patching the holes that allow them to do so without paying back into the system.