Personally, I came out to LA with only about 3 grand saved and a couch lined up on which to crash. I worked unpaid set PA gigs from Craigslist and Mandy.com for about 2 weeks, until I proved myself capable, and then started getting calls for $100/day PA jobs. After about 6 months, I was able to afford my share of a 2-bedroom apt ($625/mo in a nice neighborhood - Silver Lake). After another 3 months, I got offered a gig at a post-production house, where I worked for $125/day for about a year, then they moved me up to Production Coordinator ($250/day) and so on and so forth. I'm currently a post-supervisor at a 9-5 job making good money.
The ENTIRE TIME I was doing all of this, I have also been making films. While I was on the couch, I was writing and shooting part of "
Bloodshed" finishing it once I moved to Silver Lake. Just produced my 3rd feature, all while having a day job.
MY personal advice is to look for jobs IN THE BUSINESS OF FILM. You WILL have lean times, but - for me - making my living in the entertainment business, even though I'm mostly in commercials, has put me in contact with every single friend and collaborator I now know. Think about it: you're making a low budget film, right? Well, if you're a PA on commercial shoots, you'll be in contact with crew that are starving for well-written, non-commercial projects. Once you're in post, find a gig at a post-house, where you'll have access to decks, editors and VFX artists. Worked for me, anyway, and saved me tens of thousands of dollars.
When I first got to LA, I had several people tell me it takes 3 years to finally feel like you're in a good spot, with a job that both pays well and allows you the freedom to do your own thing. It is uncanny how right they were.
This town is awesome, by the way. You have every opportunity to succeed at your fingertips.