Specialisation= industry expertise as well as functional expertise.
Need to focus and brand yourself as, say, a PM in the Real Estate Insudtry.
Ofcourse they need to have the need for you, but the US is such a large market, there is just about anything over there - it will take a lot of patience though, as they are still struggling on the jobs front.
The above poster said that connections are important. I would say that this is the most important factor in getting a job over there.
Indeed, most mba programs heavily sell their connections ( alumni, contacts with hiring managers, companies that do on-campus recruitment etc). This , to this day, is one of the prime reasons why one does an MBA: the connections you get open doors. Hence why its so important to do one from a reputed university as their networks are usually better ( size, quality, variety).
One more thing: US companies are very reluctant to even look at candidates that require any sort of visa sponsorship. And why not- there are many US candidates on the market who obviously dont require it ( and are usually almost/just as good), and the paperwork, lawyers fees, and hassle to file with US dept of Labor just aint worth it. Hence again, having someone pull you through is extremely important.
Make sure that, if you do an MBA, then do your research upfront- have alumni gone to the US, is the career services dept helpful in this regard, are the companies recruiting open to US positions etc...If your end goal is to work in the US of A, then you need to plan your activities to get there with focus and persistence. Even in a best case scenario, it will take months.