Your referred to hiring a couple of cleaners.
If you hired somone to clean your home, and your paying them, they got to fill out one of them nice and dandy tax forms. I have a cleaning lady, and yes, I got her ID. Its the same exact situation as somone who hires a nanny, and doesn't check for tax purposes (I.E. the equivalent of paying under the table).
I'm going to assume your "burrito" remark was meant literally not as a figure of speech.
Also, if you hire somone to dump your garbage and they use illegals, yes you can get in trouble (see Wal-Mart, hiring a firm to clean the store that employed illegal aliens).
When I use contractors to do work for me, I do verify to make sure that if they sub-contract it out, its not going to illegal aliens.
My immigrant employees aren't illegals, and they pay taxes, I don't think its to much to expect others to do the same.