in canada, what you call an "undocumented immigrant" would not receive any kind of healthcare benefits. like, at all. i believe you need to present citizenship to get a health card, but don't quote me on it.
this is one of those issues that a room full of politicians is going to instantly jump to pandering around in the worst possible way, but has anybody really thought this through?
suppose that somebody is in the united states legally but temporarily, either for the night (as i often am) or for a job or for a vacation. does that person get health benefits while they're there? if so, what are the criteria for gaining access to the system?
you could argue it's a human right, but, see, this is where that argument gets messy, because when you've established a right you have to be consistent about it. if your argument is that health care is a human right and therefore everybody should have it, you'll need to get used to people entering the country for the health care system. and, this is something that we do deal with here in canada.
you could argue that it should be a residency requirement, then: so long as you have an address in the united states, you can get access to the system. but, what do you think happens, then? and, how do you treat people without a fixed address?
so, do you want to incentivize entering the country illegally? do you think it's a good idea that illegal entry gets you better health care than legal entry?
again: i'm a socialist and not a progressive/conservative, so i'm more interested in the labour side of the equation than i am in faith through works or something of the sort. i actually would put stronger labour regulations - including a stronger enforcement of minimum wage laws - ahead of migrant rights, in terms of precedence and importance. if you actually start enforcing the labour laws, you'll find the demand for migrant labour start to dry up, which is what the socialist side of the equation wants to see as the end goal. but, jumping to giving health care to non-citizens out of political expediency seems to be hastily thrown together pandering and ultimately rather poorly thought through, doesn't it?
the focus should be on getting citizenship rights to the people that ought to have it, and getting the people that ought not to have it out of the labour market. good luck with that.