I don't know how much these things vary within the EU, but from my own experience coming to Austria, as long as you can find a job in which you earn more than ~34k Eur/year (a bit less that 50k Usd/ year - not very difficult at all to do as a programmer) and have at least a bachelors degree (better a masters), getting a work permit is not that difficult.

Their work visas are actually rather difficult to get and strict.