I (trying to save myself money) tried to fix my furnace(carrier 9000) model. During the process I broke the rollout limit switch(mistaking it for the ignitor). I called local repair man he came out cleaned the ignitor/checked all the faults and so forth... but he didn't have any of the limit switches that I had broken. He said it would be approximately four days before he would be able to get one. Needless to say it is 20 degrees outside, and I need a furnace before then. He did however show mw how to bypass the switch with a fuse. My question is, would it be okay to run the furnace for three/four days with the bypass? What is the risk that I run by running without this part?

It is not recommended to run the unit without the roll out switch BUT you will have to decide weather or not to freeze or have heat. You will have to determine what to do because it is in your control to have heat not ours.

He was showing you how so you could be the judge and he will not be liable if something did happen(god forbid). A good service tech would check to make sure the flame was not rolling out before showing the home owner how to bypass it. If it was me-- rock and roll I would stay warm.