It depends on whether the general area you want to debug was originally C code or Javascript code before it was compiled to asm.js/wasm (from C) and minified JS (from unminfied JS).
If the code was originally Javascript, you can get a non-minified version by compiling without optimizations and the (optional) closure-minifier pass, and (not sure about this) enable debug information with -g.
If the code was originally C or C++, your mostly out of luck, no matter whether this is translated to WASM or asm.js, both will be pretty much unreadable since it has first been compiled down to LLVM bitcode, and then translated to WASM or asm.js, so you lose the high-level program structure. Trying to read WASM or asm.js is both pretty much like trying to understand the high-level code structure from reading assembly code. Possible, but not much fun ;)
If I want to understand how code in emscripten's "system layer" works I usually look directly at the original source code:
For instance for understanding fflush() I would start looking here:
The Javascript parts are here:
Some libraries (like WebGL) are half C, half Javascript, e.g.: