The clutch release mechanism on the Eclipse is hydraulic, not cable, and
never needs adjusting. The problem sounds like the clutch is not fully
disengaging, and Stewart has given the likely causes. If the clutch
slave cylinder is leaking, you will lose hydraulic fluid. If the fluid
level gets low enough, you will suck air into the hydraulic lines. The
air makes the slave cylinder less effective at doing its job because it
cannot generate enough force to fully release the clutch.

Check the fluid level in the clutch master cylinder. It is the smaller
of the two on the firewall in the engine compartment (on my 94 GST it is
towards the center of the firewall). If it is very low (almost empty),
that is a good indication that either the slave or master cylinder is
leaking.

The slave cylinder is located on the radiator side of the transmission.
It has a metal line connected to it, a rubber cover on one end, and has
a steel rod that goes between it and the release fork (a lever sticking
out of the side of the transmission). Pull back on the rubber cover and
see if it is wet inside. If it is, the slave cylinder is leaking and
needs to be replaced now before you damage the synchronizers.

If the clutch master cylinder is leaking, you will see fluid on the
firewall on the inside of the car, under the dash above the throttle
pedal. If you see fluid there then the master cylinder needs to be replaced.

If it is not the master or slave cylinders, the other possibility is
that the clutch disc is warped or distorted (damaged), causing it to
drag on the pressure plate and fly wheel when the clutch pedal is
depressed. In this case the clutch disc needs to be replaced (along with
the release bearing). To do this requires removal of the transmission.

Knowing this, take a look and see if you have fluid leaks. If you do,
then you know what the repair shop should be telling you. If they tell
you something other that this, go to another shop. They may recommend
replacing both the master and slave cylinders, which would seem
reasonable to me.

Tips for driving with a clutch that won't release:
1. If the engine speed matches the transmission's, you can shift into
and out of a gear without using the clutch. Here's how to downshift:
before changing gears make a note of engine RPM (say 2000). Apply just
enough throttle so the car is neither speeding up nor slowing down. Now
you can easily move the shifter into neutral without using the clutch.
Next apply enough throttle to increase the engine speed by about
1000-2000 RPM. Now you should be able to shift into the next lower gear.
Don't push too hard, instead apply some pressure on the shifter and try
raising and lowering the engine speed (not too fast) until it drops into
gear.

2. To upshift is the same, except you let up on the throttle enough to
lower the engine speed by 1000-2000 RPM.

3a. To take off from a stop: first turn off the engine, push in the
clutch, put the transmission in 1st, then start the engine when you are
ready to take off. Be sure the release the brake before trying to start
the engine!

3b. An alternative would be to downshift into 1st as you are coming to a
stop (with the clutch depressed). If the engine stalls then you are at
step 3a.

HTH
Gyz

Oil on the clutch NEVER makes it stick...