Well, my thoughts on it are - milk the job as long as you can and save up your money while you can.

I really wouldn't worry a bit about the company, they have ways to cover the bases- unless they are a little mom & pop operation - but large companies know how to work this stuff.
If they decide you are costing the company too much - they will find a way to move you along..

I haven't been through the long term disability system - but work comp system has some similarities.

You could talk it over with the Dr and see what he knows about the whole disability process and if he's been through it with other patients.

It might help you get a good overview of the issues by reading some of other posts here. and the sticky threads.

I really wouldn't stress about the employer- but you might ask about part time or light duty options?
(After you talk with your Dr to get his ideas.)

Consult with a couple of disability attys to get their take on your situation?
don't sign with any until you check them out.