He needs to add that the deportation may not be to their country of origin.
Honestly an effort of that large scale can't possibly sort everyone out, 5 million from mexico, 5 million back,1 million from Gaza, 1 million back. . . . Since they are undocumented, we have no way of knowing where they came from. Gaza to Mexico, Ukraine to Gaza, Mexico to Ukraine, it really doesn't matter to us who goes where. Those that are here to vote illegally might think twice if they come to the realization that the worst case is not that they will return to where they come from.
You dont even really need to physically deport - you can incentivise then to self-deport quite easily:
You say to literally everyone with a newly issued social security number, or none, "oh sorry, you are paying a flat X% all-income tax, and are barred from benefits from now on, but flights of emigration qualify for a one year tax rebate, as a one-time parting gift"
This way people can prove themselves legit, leave, or stay and pay a bit more tax and but be understood by everyone to be someone who is paying their way, or, at least, not taking. Meanwhile everyone else pays an even lower, or zero income tax. Now you have a system that automatically reduces immigration of unskilled people, increases respect for those who stay, massively reduces the tax burden on actual citizens. Just introduce that on day one, then sell icecream to the lines waiting to re-enter Mexico. Anyone here for handouts would quickly get the message that it's better to go under your own steam, than wait for the knock (or stay on a guest visa that means you pay taxes at higher rates, and get no assistance/foodstamps/anything at all)