I did the jump.. Mind you I had to put $400k on the line to do so, not really knowing what would happen. 8 yrs of not knowing actually.. BUT !!!!! it paid off late last yr, my wife and i both rec'd our greencards.. No getting kicked out now !
Forget what you're thinking. To be a cop, you need to be a citizen of the US. Best route into the country is what i did, which is an Investment Visa, E2, start up or buy an existing business, hope it does well, However, this doesn't lead to a GC. To get a GC, have either you or your wife get a job and find sponsorship. wait the 6+yrs, hope you don't get laid off, or marry an American once you're out here, and cut through all the red tape.
So bottom line, unless you have money and are not afraid of a little entrepreneurship , or are lucky enough to work for a company who's willing to transfer you, OR have an American g/f who's willing to marry you, then probably best forgetting about it.. BUT it can be done, and I'm living proof that it can so good luck !