Deviant, I wish I can say that the VA will expedite your claim due to harship just in time to avoid eviction but that probably won't happen. I will say to you that I've been right where you are now, things getting bad and waiting on a claim to give me some breathing room to get back on my feet. I was told by the VA when I went to them and asked for help, that I was not homeless unless I'd been homeless for thirty days; also that if I was on drugs or an alcoholic they could admit me for detox for a few days but that was it. I ended up sleeping in my car trying to keep my job which I eventually lost. I was eventually awarded my claim about six weeks later, which helped me get back on my feet and into an apartment. I was ignorant to the resources out there back then.
My advice to you is try to get to the nearest Vet Center in your area they are great and will do all they can to help you, both mentally and physically. Swallow your pride and and apply for the services that it seems you are eligible for i.e. food stamps, SSI, SSD, the food stamps will keep you eating, while you wait for your claim to come through. Some states offer Vets a one time payment of rent to avoid eviction, you can find that out at your local DHS office or the Vet Center or DAV.
Today I am IU and am able to pay my child support and my bills with a little left over, it can and does get better I'm here as proof of that. Take advantage of this site it is great and the people here are just like you, so we understand. Hope this helps God bless and hang in there.
doc/