I've been using Chrome for a good while now, and you have to explicitly enable souce map support in the options.
I'm testing something in Firefox now with Firebug, but I'm not seeing my original source files - just the generated bundle.
Is there some way to enable source map support in Firebug? I'm using Firebug 1.12.8 in Firefox 27.0.1.
Firebug doesn't support source maps yet (as of 2.0.*).
You may want to follow issue 5765 for source maps support for JavaScript and issue 5961 for CSS.
Firebug 3 will integrate into the built-in DevTools of Firefox, which already have this feature. So Firebug 3 will also have that feature. Development versions are available at getfirebug.com.
Update:
Firebug is merged into the Firefox DevTools since Firefox 48.