My maximum underwater time was about 4 minutes with the lungs fully filled with air, and I suspect that the near-blackout state I had by the end of submerging back then might be at least partially caused by excess of CO2, because I've dealt with a strong urge to breathe which disappeared prior to apparent clouding of consciousness. Fainting in a couple of minutes looks like a too optimistic estimation for me. After a normal (not maximum) exhale with prior hyperventilation I can hold my breath comfortably for 2 minutes and after that about 20 - 30 seconds feeling the need to breathe, without any sign of transition to unconsciousness during the whole period of breath holding. I didn't allow any physical activity during the experiments though, and may be it could significantly shorten the time required for achieving a blackout.