In addition to adding 127.0.0.1 localhost to your hosts file, make the following changes in Eclipse.
Under
Window -> Preferences -> Android -> DDMS
Set Base local debugger port to 8601
Check the box that says Use ADBHOST and the value should be 127.0.0.1 Thanks to Ben Clayton & Doguhan Uluca in the comments for leading me to a solution.
Some Google keywords:
Ailment or solution for Nexus S Android debugging with the error message: Can't bind to local 8600 for debugger.