Web radio with Arduino?

Hello,
Is it possible to use the Arduino board as a streaming client for web radio stations using a WiFi shield and the rMP3 shield?
The background is as follows: I want to build a jukebox, which is controlled by an old Seeburg 3W1 wallbox. The Arduino should decode the pulse train sequence from the wallbox and choose 1 out of 100 mp3 songs, which are stored at, decoded by, and played back by the rMP3 shield. I think, that's easy so far. But it would be very nice to have web radio broadcasts played back, too. That's why I want to add a WiFi shield to connect the Arduino to my router. So is there any way to accomplish this? Any hints? Any solutions?

Regards,
stefba

I would say that the arduino is no where near fast enough to do this.
Sorry.

Ok. I think that I have to rethink my plans. Either I abandon the webradio feature, or I shall use another board (beagle board, alix board), or ...
Thank you for your reply. Regards,
stefba