New clutch kit or New Cable for a 97 Nissan Sentra GXE?

I would take a look at the pressure plate and throw out bearing or possibly the sleeve the throwout rides on wore out and broke. Pull tranny or try to find some sort of inspection plate to try for a look. You might have a broken bell housing. None of these will be cheap or easy to fix.

You clutch friction plate has worn down.
You have a hydraulic system to engage/disengage the clutch.
The pressure you feel when pushing on the clutch pedal is from the clutch pressure plate, which has a series of springs you are forcing against when you push the pedal down.
As the friction plate wears the distance closes between the above mention part and the flywheel attached to the spinning engine.
Your springs on the pressure plate have limits and due to a hydraulic clutch engagements system being self adjusting the springs have been forces beyond their limits.

A complete clutch kit will run under $200 from an aftermarket supplier.
Look up a shop online as typically you'll have a clutch shop locally.

Labor can be a bit expensive. I've replaced about 6 over the years on different cars, all Japanese and it takes about 3 hours.

This picture shows the main components of a typical clutch system.
The center part of the item on the left has those springs in a circular pattern I mentioned and they have likely broken based on your description which is not an uncommon occurrence.

http://www.clutchwizadrivableages/clutch_components.png

Picture of just the pressure plate and the springs in the center.
http://www.powerstores.co.uk/imgs/store_gallery/POWER%20CLUTCH%20COVER.jpg

The can is no longer driveable.