Healthcare.gov interfaces with so many internal systems, and was subcontracted to so many parties (including big players like Experian who are exceedingly private about their software), that you couldn't untangle the hairball.

If my experience with CMS and other goverment (F, S & L) is any guide, you'd have to have extensive documentation about their particular applications running on everything from Oracle to DB2 to VSAM tables, taking input from ONC RPC calls, ZMODEM file uploads, CORBA requests, and TTY emulators. Not exactly something that you can just jump in and work on.

Beyond that, even if h/c.gov was, say, thrown up on GitHub, you couldn't just tweak some files and issue a pull request; everything has to go through FISMA audits, which make your traditional waterfall change request look like updating a blog post.