Deport 'em all, and let God sort 'em out

If I hear one more flag-wavin' all-Merkin super-patriot Constitutional 'scholar' go on about why we don't just arrest every undocumented 'immigrant' and let 'em rot in prison, I will puke. There is no better example of why we should shelve most of the basketweaving and mudpie-making classes in the modern school system, and return to a good, solid, 7th grade civics class.
Here's the deal. It ain't freakin' rocket science.
High crimes and misdimeemers ...
OK. We hear all the time that 'illegals' are de facto criminals, by virtue of their 'unauthorized presence' in the country.
First, it is in fact "... a misdemeanor according to the Immigration and Nationality Act, which prohibits non-nationals from entering or attempting to enter the United States at any time or place which has not been designated by an immigration officer, and also prohibits non-nationals from eluding inspection by immigration officers."
There is minimum fine of $50, and a max of $250, for a first such offense, and the possibility of 'imprisonment for not more than six months.'
Got it? Criminal offense, with potential for incarceration.
So why are these people not arrested?
Well ... arrest for a crime requires probable cause. You need probable cause to either get an arrest or search warrant (that pesky 4th Amendment thingie) or you need probable cause to make a warrantless arrest under one of the exigent circumstances exceptions to getting the warrant first.
You cannot assume that because you have someone with no papers, that that person has entered illegally. In order to make an arrest, you need probable cause. So how do you get that. You have Senor Mojado standing before you with no papers ... but you cannot provide a fact pattern rising to the level of probable cause that he entered the US illegally. You need real, credible info that rises to the level of probable cause. Senor Mojado is under absolutely no obligation to provide that to you; all he has to do is keep his mouth shut. It's your problem. It's that pesky 5th Amendment and 14th Amendment for you. Gosh, that Constitution thingie sho' do git in the way of good ol' fashioned jack-booted thuggery, don't it?
Absent that probable cause, you can't arrest him. Not on a criminal charge.
But what you can do is deport him under the INA section regarding 'unlawful presence.' UP isn't a criminal offense; it is civil, and all you need there is 'a preponderance of evidence,' which is a much lower standard than 'probable cause.' But it is civil, not criminal, and so you don't, you can't, arrest Senor Mojado. It's a civil matter. But how do you know he is here UP? Because he 'no hablas?' Is that proof of UP? How many legal immigrants do we have, who 'no habla?' Quite a few, in my experience. So you still have to put together a fact pattern that rises to at least that preponderance of evidence level. If you've got the guy in jail for some crime, then you know what you have, and you can give him the heave ho fairly easily. It is not quite so simple, though, when you have Senor y Senora Mojado and a pickup full of kids and freshly picked lettuce, and no other info. Remember, this is Merika! You can't beat it out of 'em, though clearly, in the minds of at least the Trumpkins, it's the Merkin thing to do. Interestingly, the 5th Amendment protection against self-incrimination applies to criminal law (the clue there being 'in-crim-in-a-tion') and not civil law ... but, Senor Mojado no hablas.
You can 'detain' Senor Mojado for deportation once you figure out he is UP, but what's the difference between that 'detention' and 'incarceration'? How long can you keep him 'detained' before it becomes an 'incarceration?'
That's a simplistic look at it. Immigration law is very complex.

But don't take my word for it. Here's a good examination of it on FindLaw.