I don't think I have seen any fan say that, on here at least. In fact, most are well aware and are ready to say she's not got the best voice. Also what are these "million" attempts? X Factor and the cameo in a film is about the only things I know she's done, and I wouldn't say the cameo was her idea of trying to "break America".
Yep of course she has tried. Her management i.e. Will.i.am has tried so hard to get her noticed in the States but it has never worked out, which is why on his albums he has only had high profile artists as he knows this will sell