In the past, I have jumped through a number of different hoops to digitize streaming audio (e.g. NPR's Car Talk using RealPlayer). I've used WireTap, but you can't set it to a timer and it won't encode MP3s. I also used Soundflower or Jack to route the output to Amadeus II, which has a timer and does MP3s, but it's such a hassle to set up when I don't use Soundflower for anything else. Or I've tried the trick of patching the output mini-jack to the input mini-jack, then recording in whatever app I choose (make sure Playthrough isn't selected). This is also a hassle (finding the cable, checking levels to make sure it's set up correctly, etc.).
But here is the easiest and quickest solution, bearing in mind I'm not going for high quality audio, just intelligible voice: Speaker to internal microphone. Connect to the website stream and, as soon as it begins playing, launch your favorite audio recording program (Audio Companion, Amadeus, Sound Studio -- I usually have one of them running all the time), and start it recording. Bingo, done.
Turns out that the internal microphone, which is usually my default setting, does an acceptable job of recording the built-in speakers. No additional routing required. Record with a timer (Amadeus II) set to the length of the stream, encode to MP3 in real time or on save. Much easier.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20060331030358926