Ha! This sounds familiar. We were trying to be tough and delay turning on the HVAC as long as we could. We live in a place where it doesn't snow, how hard could that be? Two and a half weeks ago, we were hosting a party and many of the guests were elderly, including two 92 year-olds, so we decided to turn on the heat. Zip, zero, nada.
Our house is only ten years old, so we weren't expecting this. DH did his research and ordered a new control board. He forgot to opt for expedited shipping, so the damn part took eleven days to arrive. During this time, we had a cold snap. It got down to 55 degrees and hovered between 55-58. One day, it was warmer outside than in the house, so I opened every window in the house. That got us to a balmy 61 for a few hours.
When the part finally arrived from Ohio, via the North Pole, it was a nice update, but it wasn't the entire problem. More research revealed we needed an Igniter and a (something-something, IDK). Alas, one of the parts wasn't in stock anywhere. When DH finally found one, he had to pay retail for it, bleargh. DH remembered to expedite this time and we got the parts in two days. The day after delivery, we finally had a working HVAC system, thank Dog. A couple dozen trips into the attic and $300 in parts & shipping later, we can feel our fingers and toes again.
Tl;Dr - Our house has a gigantic great room/kitchen, about 30' x 30' with 14 foot ceilings and travertine floors. It takes a long time to heat up. (Fortunately, it stays cool in the summer. We haven't used the A/C in over a year and typically only crank it on once a summer for 4-5 days.)
68 daytime, 65 at night. There is always someone home during the day, and letting it get much colder overnight makes the HVAC work a loooong time to warm it up again.