Wine and X are open source; that's all you need.

Wine Is Not an Emulator, though - you'd still need some kind of layer translating the x86 binary to JS.

wouldn't that be the role of asm.js?

No, asm.js is just "an extraordinarily optimizable, low-level subset of JavaScript". It doesn't run x86 machine code, you'd need to convert it (or interpret it).

According to the webs, there are some x86 → LLVM converters, and then Emscripten can convert LLVM → asm.js, but getting that to work would probably take many months.

Oh yeah true.