They are doing that with NativeClient. It runs x86 assembly and LLVM IL in the browser. Supposedly they'll even make it work in other browsers than Chrome.
I think that browser "assembly" code, like Dash, would have to support this, particularly if it is meant to be an alternative to compiling to JavaScript.
Also, there's really opposition of having it implemented in other browsers, at least Mozilla vocally opposed it. I think that if they managed to do it via a plugin though, that could work.