I graduated (undergrad) in Dec. from a strong non-engineering university in CS w/ no internship. I got interviews and eventually a job by making a list of companies that i'd want to work at (based on my background, passion, etc), then finding contacts at those companies to inquire about them hiring jr engineers. A good place to start is the monthly 'whos hiring' post, because a lot of times those comments have contacts attached to them. Unless the post explicitly states "no new grads" and you like the company, add it to your list. if there are companies on your list with no contact, use LinkedIn to find engineers there, then search for their personal sites/blogs for an email address.
Once you have your companies and contacts, start sending cold emails. Give them links to relevant projects and see if their company is open to hiring jr engineers/post-grad interns (a lot of people will appreciate your humility here) and if they'd be willing to get coffee with you (if you have the chance to get there physically). I would group a bunch of these meetings together then buy a flight to a city for 48hrs and just bounce from meeting to meeting getting to know engineers and seeing if they are the type of people I could work well with. If you jibe well with them, your first round interview is already done.
Although engineers will remain in high demand, finding a job is all sales and a lot of work. People in this industry are some of the kindest around, but they are busy. make it as easy as possible for them to help you out and they will. Afterwards, regardless of the outcome with the company, thank them and stay in touch. Once you do find a job, let everyone who was willing to help you out along the way know. They'll remember you in the future when they're looking to fill experience-unlimited roles or for when you're ready to move on.
Also, if you are ever in LA let me know!