Intermittenly, the furnace responds to thermostat call for heat but the blower does not come on.

Take the cover off the burner compartment of the furnace. Obtain the make and model of the furnace off the rating plate in the burner compartment and post it here.

Observe the sequence of events that occurs at the furnace when you turn up the thermostat and post that sequence of events in order and in detail.

It's a Nordyne/Miller M3RL080A BW. The problem is not predictable and only happens on occasion. Someone suggested that the problem may be with the fan control relay on the control board; what do you think?

I think that guessing is not a substitute for correct diagnosis of the problem. Also, I predict that the problem will get worse until the motor won't turn on at all.

Intermittent problems are the bain of furnace repairmen, but usually you don't have to wait around for them to display the problem.

In your case, I'd take the cover off the burner compartment and fan compartment. Turn the fan wheel by hand and tell me if the fan wheel is turning freely or if it's stiff and hard to turn.

Turn up the thermostat to 80 degrees so that the thermostat is calling for heat. Push in the door switch so that the furnace starts when you are pushing in the switch.

Carefully observe and report here the sequence of events that occurs, including the sound of any relays that turn on to energize the fan motor and whether the fan motor starts easily, whether it starts only after humming, whether the motor overheats and gets hot to the touch and any other details you observe.

Kepp cycling the furnace until you are well acquainted with the series of eventsa that occur when you push in the door switch. Keep cycling the furnace until the fan motor fails to start, and report on any discrepancies in the sequence of events that takes place when the motor fails to turn on.

You might need to start the furnace twenty or thirty times before the fan motor fails to turn on.

Can you turn the blower to on at the thermostat and the blower runs? If yes you have a control board that is bad. The good thing is you can set your thermostat to heat, set your temp and let your blower run all the time until you get your board replaced. I keep my blower running 24/7/365 for the last few years.