I have tried the WaveInput route for SqueezeCenter, but due to a non-cooperative sound card and various problems with permissions related to SqueezeCenter running as a limited user I decided to go another route and stream sound from my Linux laptop via Icecast. If you want try using WaveInput and have the same problems with recording from the sound card as I have (it plain doesn't work with arecord and friends) there is a recipe here that might work for you.
I need to use PulseAudio to get recording of sound played through the sound card to work as my Intel sound card refuses to allow me to record the sound directly. Luckily PulseAudio finally works OK for me now. I configured Wine with padsp winecfg and chose the OSS output driver for sound (ALSA works poorly at the moment). Now, run Spotify as padsp wine spotify.exe. Spotify should pop up in your PulseAudio Volume Control (pavucontrol) in the Playback tab.
You need to define a PulseAudio sink that is different from the normal (output to PC speakers). I chose to call this sink spotify. Create the sink with the following command.
pactl load-module module-null-sink sink_name=spotify
The sink should pop up in the volume control under the Output Devices tab. Next, select this sink as the default for Spotify in the Playback tab (click the small down-arrow and choose Move Stream and then Null Output).
You can run Icecast with a minimalistic configuration. I used the minimal example (/usr/share/doc/icecast2/icecast_minimal.xml.dist on Ubuntu) where I modified the passwords and the log directory (I set the log directory a directory where I have write permissions so that I can run Icecast as my own user). Start Icecast with
icecast2 -c icecast.xml
Finally I take the spotify PulseAudio sink and channel it to Icecast by use of Gstreamer. The magic command is (in one line).
gst-launch-0.10 pulsesrc device=spotify.monitor ! audioconvert ! vorbisenc bitrate=300000 ! oggmux ! shout2send ip=localhost port=8000 password=PASSWORD mount=stream.ogg
The bit rate is set to the highest I could use without getting error messages (300kbps). I assume this is pretty transparent and does not degrade the 160kbps Spotify output much.
Now tune your Squeezebox to URL http://ip-address-of-linux-machine:8000/stream.ogg. Modify the file name and port according to your configuration.
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Update 2013: I no longer use this method and do not know if it still works or if there are better ways to do this now