A furnace will give off a signal that tells you that it needs to be switched off. This can either be as a result of just being turned off or it could be when the fuel gauge reaches zero. Either way, a furnace has to be switched off in order for the air conditioner to kick in. You could also try to restart it by manually turning it on and off but you could run the risk of a fire as well. Many people simply turn off the fuse box or power supply, instead of attempting to switch it off as they would if they had tried it before.
If you find that your furnace has just quit, you will need to contact the dealer who sold it to you. The dealer will be able to help you find out what the reason was for the furnace not starting. You will need to determine whether the furnace is faulty or the fault of someone else. Most commonly, a faulty furnace will start automatically after a short period of time. It will start making sounds to tell you that it is working but the actual function of the furnace is not working properly. In some cases, the problem could be that the blower motor is not functioning as it should. You should call the service station where the blower motor was manufactured if the problem is not repairable.
The problem with a furnace that quits on its own is that the furnace cannot perform its normal functions without the aid of an air conditioning unit. A power outage will cause the furnace to go off and will likely ruin your air conditioning system. This will cost you a lot of money in the long run if you have a central air conditioner.