The problem turned out to be a clogged nozzle on the draft inducer. (I had a suspicion that this was the problem because we had a similar issue a few years ago and had to call a technician). On our particular model of furnace, there is a vacuum hose that runs from the draft inducer to a pressure switch that regulates when the furnace will light. Because of the clog, the switch would not activate. I was able to diagnose the problem by pulling off the hose and, after checking that there was no obstruction in the hose, sucking on it to see if I could get the switch to activate (which it did). Fortunately, after diagnosing the problem, it was easily remedied using a wire to push out the blockage and reattach the vacuum hose. (Additional information about pressure switches on gas furnaces can be found here).
However, in starting and maintaining the fire in the fireplace, I was once again impressed with the need to have different types of wood. I'm not just talking about kindling, small pieces, and larger pieces, but woods with different burning characteristics.
I've mentioned before that a lot of the pine wood we've used in this area, unless it impregnated with a lot of pitch, generally does not release a great deal of energy when burned. These pieces, at least when larger, are good for burning for a long period of time. However, to get them to combust completely generally requires mixing some hotter burning wood in the fire. We use fruit tree wood, poplar, and/or ceder that we salvaged from a fence.
We also use the hotter burning wood to get an initial hot fire going. I've learned that it is far better to get a larger, hot fire going that quickly warms the house up, and then use smaller quantities of wood to maintain the temperature, than to be parsimonious with the wood initially and never reach the desired temperature.