You can't get the dole if you are an illegal immigrant --> you have no ability to sign up.
We have a relatively minor problem with illegal immigrants. There are quite a lot of overstayers (it is easy to come visit, but less easy to get a permanent work visa), often Pacific Islander or Asian, who generally stay with, and are sometimes supported by, family members. We don't have the same issue you have with Mexico or Australia has with boat people - we are in the middle of nowhere so illegal migration en-masse isn't an issue.
I mean, there is still a problem - the newspapers a couple of weeks ago were full of articles about a guy who is in the country illegally, is being given state funded dialisis and has been arrested a couple of times for beating his wife. He can't be sent home (to Tokelau I think) because he will die without the hospital access he currently has.
Assisting the poor
it artifically drives up the clearing price of rents in Los Angeles
Yeah, I agree, it does. What is the alternative though? Either the rents drop to what can be afforded without govt intervention, or they drop to a point where there is a sort of substandard equilibrium, with increased overcrowding and/or financial hardship (ie, too great a percentage of income being spent on rent). While I don't doubt a (more efficient) equilibrium would be reached, my feeling is that it would be a socially unacceptable one.
Maybe with less government hand outs, people would tend to fend for themselves and their families more.
I think this is a myth about poverty. For every person one can find who is poor, lazy and feeding off the system, I would expect to find at least one person who works there ass off in a low income job and still struggles to make ends meet. Poverty in the US (and NZ) doesn't mean going without food every day, etc, but it means a pretty low quality of life ---> have a look at the map on the link below and assume that if someone is below the poverty line they are lacking in at least some of the basics required for life, and have few, if any, luxuries. They will also have reduced access to healthcare and education.
http://www.usccb.org/cchd/povertyusa/map.htm
I guess I come from a viewpoint that I don't care where people who are in poverty come from, how they got there, or whether they are there because of there own mistakes or bad luck. I just want to have a society which has structures to look after and educate (ie fix the problem). If this means there is a certain percentage which abuses the welfare system, then I can live with that.
The other "myth" is that people don't try to work their way out of poverty because it is too comfortable. Look at the income levels listed here - being below these income levels would truely suck, and offers plenty of motivation.
http://www.usccb.org/cchd/povertyusa/povfact9.htm
Alternatively, for the pretty multimedia:
http://www.usccb.org/cchd/povertyusa/tour2.htm
(sorry for the long post - I organised and presented a whole bunch of stuff on poverty in NZ last night to a youth group, so I am full of info right now...)