As you have noted a snootfull of CO2 is quite painful but that isn't enough to protect you. If you go blissfully charging into a room that is full of CO2 exhaling while on the way in and inhale for the first time while you are well within the room I understand that O2 will pass into the CO2 so fast that you will pass out before you can get back to the door (this happens with other gasses too).
Yeah, this might be even worse with CO2. In normal respiring tissue the production of CO2 causes the blood pH to drop which lowers the affinity hemoglobin has for O2 which causes it to dump O2 into the blood. Normally this is good since it causes O2 to be released near the tissues that need O2 but in a room full of CO2 it will just accelerate O2 leaving the blood.
Anyway, if you calculate the maximum amount of CO2 that a batch of beer could possibly produce (assuming all the sugar was converted to H20 and CO2) it might be enough to become worrisome if your basement has absolutely no circulation. Most likely the air circulation is orders of magnitude more than enough to deal with this. In terms of raw CO2 production, a gas furnace or stove probably pumps out as much CO2 in a minute or two as an entire batch of beer will produce.