I have a 2002 ls1 and every morning when I go to start the car the clutch depresses to the floor. After few min of the car warming up I can get it to come back up. Sometimes all I have to do is pump on it and build up pressure. This happens only overnight

 

are you losing fluid? sounds like you have a leak. could be in the line or the master or slave cylinder is failing. if your not losing fluid then i would say that one of the cylinders is failing and letting fluid get by the cylinder and back into the system.

 

You descried perfectly a hydraulic condition know has a hard seal. The fluid will leak past the seal until things get warmed up or flexed a few times. If you are not losing fluid then this must be the seal in the master cylinder. When the compression seal in the master cylinder leaks it just leaks back into the reservoir.

At one point with the LT1 cars the cheapest place to the master cylinder was the dealer. They sold the whole system Master slave and hose for like $130. Not sure if that is still true or if it was ever true with the Ls1. Might be worth a phone call.

 

I priced one at the parts store and they are around $65. Not checked the dealer. It does not happen everyday. Only on very cold days. How hard is it to change the master cylinder and does the whole system need bleed