This is something I think a lot of people miss when it comes to discussing the Homeless problem. IMO, there's 4 demographics of homeless.
Yes, there are people who are genuinely down on their luck, but it's a minority compared to both people who are mentally unwell/addicts, and people who chose to be homeless for one reason or another. People who are down on their luck aren't the ones who are living under overpasses and sitting outside of McDonalds all day asking for $10 every other hour.
There are people who actually "make a living" off of panhandling and they make more in a day than some minimum wage workers do in a week. There's been studies/interviews/ whatever about how people will essentially "dress up" like a bum, make money, then call a friend to drive them back to their upper-middle class suburban home.
There are of course the druggies and mentally ill. If you're sympathetic you can argue that they are "poor victims" of circumstance, but they seem to be "poor victims" who doesn't want help, and no one wants to help.
Lastly, there are actually people who just enjoy the "nomadic" lifestyle. Yes, they're still a burden on taxpayers, but it for the most part those types generally stay to themselves.
Of the four groups, I only feel sympathy towards the "down on your luck" types, and I'm fairly indifferent to the "nomad" types. That said however, those two groups, I'd wager, only make up about 5% of the homeless population.