I would contact first off, The American Red Cross (they have programs for people without income, and at risk of homelessness, you may qualify), also St. Vincent De Paul -- Catholic Charities. You don't have to be Catholic, and they can offer rental assistance. They also have a lot more resources for assistance and can help direct you in the right direction. They've helped me out with food and utilities, when i was in danger of losing them.
There are a lot of organizations for women in danger of being homeless -- and though it says for women, it also includes their familes (spouses, fiances, children etc) but you would have to be the one to seek assistance.
I would definately contact Legal Aid in the area, and get some legal assistance on the eviction issue. It is pretty standard that if you go to court, with atleast one month of rent, the judge often will make a judgement in your favor, that could help until you get another job. But you have to go to court, and bring what money you can. ALSO, if you can get your landlord to accept even SOME money, and get a receipt, it would null and void the eviction as if they accept a partial payment, they can't evict you. I've worked in the housing industry and can tell you for a fact, this is the case. Most managers know this and don't accept anything other than the full amount, but you never know -- maybe yours doesn't know.
I would definately try to find a place now before the eviction proceedings, because once you have an eviction on your record, you're going to have a really hard time, unless you go to a trailer park or something...
I've got pets too, so I wish you lots of luck, because i would've lived in my car, if i hadn't been able to find the money...You could also try some day labor, where they pay you every day for what work you do. There are a lot of those places in phoenix area, and though not something most would want to do, if you're desperate they are a God-send. Have either of you applied for unemployment? Food stamps? SSI? things to consider