If anything, nanny wages will skyrocket. Lots of families will need to take care of their own children.
Agree with others that the opposite will occur in areas like DC where employers pay on the books. I know that when we were hiring there were a few candidates that I really liked but they weren't legal so we had to knock them off our list. The pool of our favorite and legal candidates was therefore smaller. While we weren't looking for a lower rate, if we had been choosing among 6 good legal candidates rather than 3,it would have meant that we could negotiate a lower rate.
It may not affect areas outside of DC where paying nannies under the table is the norm. There is an incentive for the nannies to under report their income to get access to services and take more money home. There is an incentive for employers not to deal with the hassle of taxes and say 7.5%. There is little chance of either side getting caught so I doubt immigration reform will change the market in these areas.