I learned that I'm not the only one having problems with the White House "RSS" (really Atom) feeds. My feed reader (a very, very hacked up version of TT-RSS) populated the database with a single entry from the White House blog feed, but never loaded any more articles, though examining the feed "by hand" shows that there are new entries.
After doing some digging around, I found that the same things that Rogers Cadenhead found (before I found his blog entry, of course). The "id" attribute of each entry, used in the TT-RSS schema as the primary key for the row in the "entries" table. Lovely.
I know there are a lot more pressing problems for the U.S. Federal Executive than fixing their "RSS" feeds, but surely it's somebody's job to work on this. Please fix your feeds.