Is it not enough that once they get a job and begin earning, they will be paying taxes like the rest of us?
It would be better and probably far more cost effective for the government to simply loan money when major healthcare is needed to those that can't pay. At least the government isn't forcing them to become debtors until their health dictates that they do so.
You assume that they're telling the truth when they say they want to "help" the poor.