I've been running on emergency heating for 3 weeks due to my outside heating unit not working. But now it feels like the house doesn't warm up anymore. How long can you run on emergency heating?

Basically until you can't afford to pay the electric bills or it breaks.

Have you checked your filters?

Yeah I checked the filters. Its just frustrating because I have two small kids and my landlord is taking for ever to fix the outside unit.

Is the temprature in the house being maintained at least? I can understand the frustration. Been there a few times over the years. Hard to guess what the delay is... may be a place waiting for parts, or to find time to actually get there. Extremes in weather tend to overwelm these places with calls for help.

As a renter you have right. If you had heat when you rented the place the landlord has to keep it going. Its not hard to find parts or a company that will show up. Just about all service companies offer 24 hr. service. Just about any supply house will have a drop in for any part-- defrost boards, fan motors, compressors and so on. Keep calling your landlord. He needs to stay on top of it and make it right.