The official website of Congress (Congress.gov) which replaced Thomas.Gov, has the text and status of most bills, but no API. As this article explains, the goal of modernizing the website didn't take open standards very far.
In addition to https://www.govtrack.us/ which does have an API, you may want to also check out the non-governmental http://www.opencongress.org/ which has similiar data. Specificially, Open Congress tracks bills and has a link http://www.opencongress.org/issues for issues, which they have aggregated in one fashion.
Beyond that, developing an "official" taxonomy for bills maintained by a governmental organization will most likely, be quite difficult. If open to government oversight, the pressure for a congressman to game the system with its labels would be significant, reducing its effectiveness. Depending on whether an interest wants the bill to be more or less well known (directly affecting its chances of passage), the temptation to fiddle with its classification would simply be too great.