A house that tight should
A: only use sealed-combustion direct-vented type heating appliances- relying on conditioned space air for combustion in a super-tight house is a recipe for higher carbon monoxide in the exchaust and potential backdrafting.
B: have an active ventilation system for ensuring a minimum level of air exchanges in the house (preferably a heat recovery/energy-recovery type venilator. ERV, if you're anywhere near the gulf-coast, since it'll strip some of the summer humidity out of the ventilation air where HRV won't. The humidity is less of an issue in the panhandle or west of the Pecos than it is from the Red River valley down to Brownsville. If your summertime outdoor dew points are north of 65F most of the time, ERV is by far the better bet.)
Atmospheric-drafted units need to be carefully assessed for backdrafting potential. Run all of your bathroom & kichen fans and the closthes dryer too, and use a smoke-pencil or incense or something to verify that no air is coming back down the exhaust plumbing on the burners, both when firing and not. If you have central-air or hot-air heating, test with & without the air handlers running as well.