It seems that (P)NaCl could be pretty close if you can, for browsers without it (same as not having asm.js), compile the LLVM bitcode into Javascript, which I think is possible with Emscripten (also what compiles to asm.js).

You would probably want some sort of layer to abstract away the NaCl API so you can call the equivalents for asm.js, but I don't actually know that asm.js has equivalents.