For me, it was a numbers game in the end. There were enough opportunities out there but I found for every five applications I submitted, I'd get one callback. In the end, it took me around five weeks to get the job I wanted (and I was being a little fussy about job location and salary). Looking for work becomes a fulltime job in and of itself, but it's worth putting the effort in.
My degrees didn't prove to be the stumbling block. It was my Australian experience they didn't quite understand and why I was in the States. So I made sure my resume was very clear and I stated in my resume that I was a lawful permanent resident (makes a difference as, if you're an LPR, they don't have to do any work with visas). Oh, and make sure you pick somewhere to live where there is work. Where I was, there were upwards of 20 new roles a day, so I was spoilt for choice.