With only 3 years experience in the USA, you would look for CRA2 jobs (seniors usually have 4-5 years at minimum). US CROs do visas, but if they had to chose from someone who needed a visa and someone who didn't, they would pick the person who didn't need the visa. So, with the poor US economy, you could imAgine how hard it will be, but not impossible.
I would first get a job with a US CRO who has offices in Russia. After you prove yourself to thecompany, ask for relocation from the RUssia office to another office in the EU or USA. That way, you'll know you like the company prior to moving halfway around the world for a job you may not like.