The furnace draws about 12A.
How long it will run on batteries depends on the outside temp, the temperature you set on the thermostat and the battery capacity you have.
For example FLA batteries have only 50% usable capacity (down to 12vdc approximately) before you begin to deplete their capacity (shorten their lifespan).
So a 100Ah FLA battery will run the furnace about 4 hours continuously before dieing.
Lithium batteries you can run all the way down, although I don't recommend it. I try to stay between 10-90%.
A pair of 100Ah Lithium batteries should get you through the night.
Excellent article on Lithium batteries
Just be aware of using them at freezing temperatures.
How to find happiness with lithium batteries
https://www.solacity.com/how-to-keep...tteries-happy/