As previously mentioned, the difficulty is in obtaining a Green Card or any type of Work Permit, permitting legal employment. Although I do know of individuals who have been in on Work Permits, they are few and far between. (Some of them were one-way bogus deals).
Green Card lottery is one way in, not too many options beyond that. I occasionally get resume's from the UK, but none with the right to work. We cannot get work permits for maintenance personnel, OR pilots.
Try writing to Operators, you never know who might have something on the go, you won't find out until you try.
You should also look at getting your A&P licence as a pre-requisite for entering the US aviation business. The regulations are straight forward and clearly defined, all are available on the Internet. You can study tourself, and gain an A&P.
There are also A&P schools offering full time 1 year courses, leading to an A&P.
I am not sure if these schools are able to offer visa's that permit employment, but it might be worth looking into.
Good luck. Its a pretty good business over here, if you can get a decent job. There are excellent rewards, but you need to work hard to get them!