Knowingly employing an illegal alien is already a felony.
"I am perfectly of your mind, that measures of great Temper are necessary with the Germans: and am not without Apprehensions, that thro' their indiscretion or Ours, or both, great disorders and inconveniences may one day arise among us; Those who come hither are generally of the most ignorant Stupid Sort of their own Nation, and as Ignorance is often attended with Credulity when Knavery would mislead it, and with Suspicion when Honesty would set it right; and as few of the English understand the German Language, and so cannot address them either from the Press or Pulpit, 'tis almost impossible to remove any prejudices they once entertain. Their own Clergy have very little influence over the people; who seem to take an uncommon pleasure in abusing and discharging the Minister on every trivial occasion. Not being used to Liberty, they know not how to make a modest use of it; and as Kolben says of the young Hottentots, that they are not esteemed men till they have shewn their manhood by beating their mothers, so these seem to think themselves not free, till they can feel their liberty in abusing and insulting their Teachers. Thus they are under no restraint of Ecclesiastical Government; They behave, however, submissively enough at present to the Civil Government which I wish they may continue to do: For I remember when they modestly declined intermeddling in our Elections, but now they come in droves, and carry all before them, except in one or two Counties; Few of their children in the Country learn English; they import many Books from Germany; and of the six printing houses in the Province, two are entirely German, two half German half English, and but two entirely English; They have one German News-paper, and one half German. Advertisements intended to be general are now printed in Dutch and English; the Signs in our Streets have inscriptions in both languages, and in some places only German: They begin of late to make all their Bonds nad other legal Writings in their own Language, which (though I think it ought not to be) are allowed good in our Courts, where the German Business so encreases that there is continual need of Interpreters; and I suppose in a few years they will be also necessary in the Assembly, to tell one half of our Legislators what the other half say; In short unless the stream of their importation could be turned from this to other colonies, as you very judiciously propose, they will soon so out number us, that all the advantages we have will not in My Opinion be able to preserve our language, and even our Government will become precarious." -- Benjamin Franklin
Even Ben was wrong about assimilation.
Then the problem must be lack of enforcement.
Failing to verify immigration status before employing them is not. That's why illegal immigration has flourished.
Gingrich just sad that no employer was taken to task last year for employing illegal aliens.
We have a big problem with enforcement.