Jollero,
Take the amp-hr rating of your battery (for easy math, lets just say it's 100 Amp-hrs.
Divide by your power usage .... 12 Amps (you can ignore the CO detector for now because it represents so little of your total usage).
This yields a result of 8.3 hours.
This means that if you run your furnace constantly, a new, fully charged 100 Amp-Hr battery will be completely depleted in 8.3 hours.
Fortunately, it is likely that your finance doesn't run constantly, and perhaps is only on about 20% of the time. So dividing 8.3 hours by 20% (0.25) you get 41.5 hours.
While this initially sounds great, something to keep in mind is that your battery will last much longer before it needs to be replaced if you don't use more than about 1/2 of it's total capacity before recharging.
Hence, multiplying 41.5 hours by 50% (0.5) gives you 20.8 hours.
So, with a single 100 Amp-Hr battery running only your 12 amp furnace, you are likely to have to recharge at least once every ~24 hours to maintain good battery health. This seems to agree with the rule of thumb of "one battery per day".
I hope you or someone else finds this useful,
Steve
After posting, I see others are able to type faster than I and have also answered your question. O-well. :)