It doesn't look like GC is the only thing that stops Python code from targeting WebAssembly/asm.js. Both represent low-level statically typed code, in which Python code can't (realistically) be represented. As current toolchain of WebAssembly/asm.js is based on LLVM, a language that can be easily compiled to LLVM IR can be converted to WebAssembly/asm.js. But alas, Python is too dynamic to fit into it as well, as proven by Unladen Swallow and several attempts of PyPy.

This asm.js presentation has slides about the state of dynamic languages. What it means is that currently it's only possible to compile whole VM (language implementation in C/C++) to WebAssembly/asm.js and interpret (with JIT where possible) original sources. For Python there're several existing projects:

PyPy: PyPy.js (author's talk at PyCon). Here's release repo. Main JS file, pypyjs.vm.js, is 13 MB (2MB after gzip -6) + Python stdlib + other stuff.
CPython: EmPython, CPython-Emscripten, EmCPython, etc. empython.js is 5.8 MB (2.1 MB after gzip -6), no stdlib.
Micropython: this fork.

There was no built JS file there, so I was able to build it with trzeci/emscripten/, a ready-made Emscripten toolchain. Something like:

git clone https://github.com/matthewelse/micropython.git
cd micropython
docker run --rm -it -v $(pwd):/src trzeci/emscripten bash
apt-get update && apt-get install -y python3
cd emscripten
make -j

to run REPL: npm install && nodejs server.js

It produces micropython.js of 1.1 MB (225 KB after gzip -d). The latter is already something to consider, if you need only very compliant implementation without stdlib.

To produce WebAssembly build you can change line 13 of the Makefile to

CC = emcc -s RESERVED_FUNCTION_POINTERS=20 -s WASM=1
Then make -j produces:

113 KB micropython.js
240 KB micropython.wasm
You can look at HTML output of emcc hello.c -s WASM=1 -o hello.html, to see how to use these files.

This way you can also potentially build PyPy and CPython in WebAssembly to interpret your Python application in a compliant browser.

Another potentially interesting thing here is Nuitka, a Python to C++ compiler. Potentially it can be possible to build your Python app to C++ and then compile it along with CPython with Emscripten. But practically I've no idea how to do it.

Solutions
For the time being, if you're building a conventional web site or web app where download several-megabyte JS file is barely an option, take a look at Python-to-JavaScript transpilers (e.g. Transcrypt) or JavaScript Python implementations (e.g. Brython). Or try your luck with others from list of languages that compile to JavaScript.

Otherwise, if download size is not an issue, and you're ready to tackle a lot of rough edges, choose between the three above.