Let's start there. Illegals should not vote at all, and making sure that they do not, falls on us. At least that's the way The Founders set the whole thing up.
Article 1.
Now, unless I've missed it, the US Congress has yet to pass a law forcing the States to allow illegal immigrants to vote, it is up to each individual County to stop this from happening.
That's the first part of the answer.
The second part is two-fold.
Number one is that the total number of illegals sneaking in to vote would be meaningless if we, as citizens, would take our civil duties more seriously, and managed to get to the polls at more than 50% for presidential elections, and 37% for non-presidential election years.