Yeah, internal hackathon. But if they want to make it really work, they should do the Silicon Valley long-weekend style hackathons:
1. Let your employees decide/vote on the weekend, so as few miss it due to vacation and whatnot as possible.
2. Make it Thursday night - Sunday afternoon, and give them Monday off to recuperate/run errands/catch up on life. 8 days off/year instead of 52 should be much more doable for a smaller operation like NPR.
3. Schedule it far in advance, encourage people/teams to brainstorm ideas and have a rough project plan or three ready to go Thursday night.
4. Provide all the junk food, health food, and caffeine they can eat, free. Let them choose the menu when they're voting on the dates. Set up an internal website for all of this.
5. Make sure they've got all the hardware and software they could anticipate needing all on-site and ready go at the start. Minimize setup time.
6. Have something for planned for families as well, involve them if possible. Imagine, instead of going to watch a baseball game on the weekend with your mom and/or dad, going to a hackathon with them. Have a mini-hackathon on the side for the kids.
7. Have demo night Sunday at the end, fun/funny awards as well. For example, I dig Foursquare's 'Bender' badge for someone who goes out 4+ nights in a row. A hackathon equivalent would be whoever worked on site the longest and slept the least.
8. etc.
I don't think one work day every quarter is going to do much for them, but if they set it up like a hackathon sprint party over a very long weekend, they might get some interesting results.