Eminent social justice activist Shaun King raises a pertinent point on the current topic (in the sphere of the US presidential candidate selection process) of what to do with the "immigrants of dubious legality" in the USA:
What do you think it would look like, practically speaking, for Trump to "round up" 450,000 immigrants per month and "ship them off".
— Shaun King (@ShaunKing) October 15, 2015
This is, as several people has observed, quite a hard problem.
The first problem you have is finding the immigrants, and this is probably the killer. You've got 360M people in the USA, illegal immigrants are 10M-20M in number by various estimates, so for every 1000 illegals found you have to trawl (naively) about 20,000 legal citizens - and at 450K illegals/month constant rate you're looking at 2 years to remove nearly everyone. So every month you need to annoy 9M legal residents at some level in order to meet your quota. As immigrant numbers fall, that number of recently annoyed legal residents will rise. You'll start with unobtrusive measures, but as time goes on you'll need to get more and more intrusive - and most of the annoyed legal residents are citizens, and can vote against representatives who are supporting this measure.
Then you need to make them leave the country. Detention is expensive, ask anybody in the Federal Bureau of Prisons - average is about $100/day and that assumes amortizing entry and exit costs over many months. The sooner you can export them, the better. You need to fund daily 1-way flights from a wide range of cities to the dominant countries of residence of illegal immigrants: Mexico (obviously), major nations in Central/South America, and Pakistan/India/Bangladesh. The immigrants won't be paying for this - they'd rather pass their US$ to legal resident friends and rely on that largesse being transmitted to their home country for later pick-up, at a generous margin. So the US government will be implicitly boosting illegal financial transactions as a result. Occupancy rate on those planes is going to be highly variable. Assuming average occupancy of an evacuation plane at 50% - realistically, you can't fill them with paying passengers, ask anyone in the UK - that $700 is a reasonable round trip fare to Latin America, and noting that the return journey will need to be empty (don't even think about eating the profit margins of existing airlines, there's no way this turns out well) you're spending about $700M/month just on the export. This assumes zero cost on detention and transport to the airport, which is "optimistic".
What's the end run around this? Make the illegals deport themselves. Illegal immigrants come to the USA to work and earn money for their family, with the (faint) hope that they can eventually stay. This might occur by having a baby in the USA who will be a US citizen, and applying for residency on compassionate grounds; alternatively they might eventually find an employer willing to sponsor them. So remove that attraction. There are definite areas of employment for illegal immigrants; it depends on the region, but generally agriculture (crop picking), daily manual labour and domestic service are the top areas. Focus tax audits on those areas, reduce the marginal cost of legal labor (e.g. by increasing the deductability of costs associated with a provably legal labourer) and watch the illegal employment rate plummet.
This isn't a free ride - the government will still need to fund the free no-questions-asked one-way flights home, but if they really want to make this happen then it's probably the cheapest way to achieve the goal. With no income, and easy access to return journeys to one's home country, the labour problem will mostly fix itself.
Of course, this reduces the government benefit of illegal employment - is an incumbent administration willing to forego all the income from illegal activity?