You can compile many things to C and LLVM IR, like C++, C#, and so forth. You can compile the VMs of dynamic languages like Python, Lua and Ruby, but compiling them directly would be inefficient - you'd need type checks all over the place. You need a custom VM to be fast on those.
asm.js can run Lua at close to the speed of the normal Lua VM running natively, so this approach is very feasible. But, for JavaScript itself, it probably doesn't make sense, the current VMs are the best that can be done.
However, a subset of TypeScript - without classes, without weird prototype things, just arrays and numbers and computation on those - could be compiled to asm.js. That might be an interesting project to try out.