Have an Answer?
The best thing you can do is hire yourself. Spend whatever time you can afford on your demo reel & your portfolio site. Give yourself projects that will help hone your skills and show off your abilities to future employers. Employers want to see what you can do.
That will get you half way there.
The other half is networking as the best way to land a job is to have some sort of connection to that person.
You can this by becoming active in local and online communities in your field. Actively participate in forums, blogs comments, etc. Give feedback to others on their work and put your own work out there for others to critic. Over time you will make connections that may open doors in the future.
In the short run you should also be scouring linkedIn. Connect with headhunters and recruiters that can send potential leads your way. Connect with HR reps at any company you are interested in. Even if they are not hiring now, it may change down the road and they will look at their contacts first. Connect with other animators that work at companies that you respect and see if they can give you feedback on your portfolio.
Best of luck!