Is it alcohol and drug abuse, or is it mental problems? It's mental problems, isn't it? Wouldn't alcohol and drug abuse stem from mental problems, like addiction, depression, bipolar, etc?
Most academic studies I've read about homelessness cites mental illness as the cause.
You mistake austerity for virtue, which is not empathetic. It's just pathetic.
It can be both, but there are many homeless people who have drug and alcohol problems who have never been treated (or diagnosed) with mental problems. Regardless of the underlying cause, it is not a good idea to give them cash that can be used for drugs or alcohol. Those with mental problems aren't going to use it for psychiatric care.
Sometimes they do use money for food. There was a guy I used to see often at the homeless shelter where I volunteered. One day I asked him why I hadn't seen him for a few days and didn't he want to eat? He said he and his frieds preferred to panhandle to get enough money to eat at McDonald's at 7:00 rather than have the shelter food at 5:00.
Your debates are not based on the best public policy outcomes to help the clients but how we "feel." Empathy does not always result in good public policy.
So YOU are the liar. 
The facts remain that educating illegal alien kids is VERY expensive and comes out of the average taxpayer's pocket. A family with 3 kids can cost an average of over 35K a year to a school system. But I know YOU don't care.