If you SEND THEM BACK, they will find another way back in and just keep on going.
If you ARREST THEM, they will just be let out, and then keep on going.
If you LET THEM GO, they will just keep on going.
So, what to do?
I have a better idea. Arrange with Russia to reopen some of their languishing camps in their far north. Pay the Russkies, say, $1000 a head/year for food-clothing-shelter (they should make out like bandits on that deal!). The illegals won't even have to work those nasty old salt and gold mines or cut their impossible quotas of timber. They can just relax for the year. Then, after a year on vacation there, deport them back to where they came from, with $10 in their pockets - for their final bus ride home. If they show up in this country again, double their time in Russia, each time they show up.
Both we and our buddies, the Russians, will make out on the deal. Plus, nobody will be infesting our ERs or being born here and becoming automatic citizens (and I doubt the Russians have the same silly just-show-up citizenship deals we have).
I'll bet the deluge of illegals stops,... real quick!