Having a system where illegal immigrants are tolerated/accepted and ultimately given amnesty is not the best approach in my view. Such a system is what promoted the migrations across Europe, which caused disruption and hardship for the migrants themselves, and to a lesser extent legal residents of the countries. Such a system also creates a world in which sex trafficking is much easier, criminals offering passage to migrants in generals becomes more profitable, and those boats that sink in the mediterranean killing people also become more common. And perhaps in the US more people will die trying to cross deserts in the border area in summer. That is what happens in the Chile/Peru/Bolivia desert border area.
Also, rewarding illegal immigration is fundamentally unfair. If you apply to your local consulate/embassy for a visa/asylum but are rejected then hear of your friend illegally immigrating to the US and making a successful life there, you might feel a great sense of injustice.
So I am in favour of illegal immigrants being found and sent home, in general, and I think money should be spent on this. And I don't think there is anything fundamentally wrong with going to work places or maybe even knocking on doors or stopping people on the street and asking for documentation. Although this is debatable and is a grey area that needs to be done with tremendous care and courtesy especially as it becomes a danger of racial profiling.
I am not in favour of throwing out every illegal immigrant of course not, I think it depends on the case. If someone came to the US at the age of 3 and is now 25 then I think most people would agree that it wouldn't be fair to deport them. That being said, I don't think coming to the US as a child or baby or even being born there should make someone a citizen automatically either, in other words if a couple crosses the border and has a baby born the day after, inside the US, and then are caught a few months or a year later, then they should probably still all leave. But by the time the child has lived there a certain amount of years it becomes too cruel to deport them, and a better route would be allow them all to become legal somehow.
Of course this needs to be done in combination with an increase in immigrants being accepted via legal applications made from either their home country or a third country, and by having a system that doesn't drown people in paperwork. It also needs to be done in combination with more money spent on border police to make it harder for people to get in.
And with allowances made for people that genuinely were seeking persecution or fleeing from something terrible and had little choice. For example if someone was known to be a target for drug cartels in Mexico because they were a journalist that had published certain things, you might treat them more favourably if they took a quick, illegal route to the US.
Where illegal immigrants are caught and allowed to stay this should be done in such a way that they get a worse deal than people who applied legally in the first place, for example they have to pay a fine or triple the visa fee or a higher taxation or aren't allowed certain benefits for a a period of time. Otherwise, it's just not fair. And blanket amnesties from time to time is great news for the people making money from people trafficking.
Of course, the problem with a Trump administration, in my view, is not that they want to deport illegal immigrants (which is fair enough, they are breaking the law) but the fear that they will do it in a crass way, that they won't do it with due care for vulnerable illegal immigrants, and that this will (and yes, already has) spilled over into bad treatments of legal immigrants by Trump supporters.
But none of that changes my main arguments here.
Anyway, maybe I'm wrong, would be interested to hear what others think.
I do believe in open borders eventually, but I don't think we are there yet, but I think it should be an long-term goal.