Carbon monoxide has a tendency to remain with a red blood cell 240 times longer than oxygen does, or more accurately put, the red blood cell has a greater affinity for CO than O2.
Actually I think the story is slightly different. Oxygen is transported in your blood by Haemoglobin (Hb). Depending on subtle changes in the acidity level of your blood Hb will either grab an O2 molecule or release it. And the subtle changes in the acidity level of your blood are in turn caused by CO2 that's dissolved into the blood in organs, muscles and so forth (CO2 + H2O becomes H2CO3 - an acid) and released into the air in your lungs.
However, Hb has a far greater affinity for CO than for O2 so if any CO is in the air the Hb will suck that up instead. But this bond is so strong that the subtle changes in acidity won't release the CO. In effect, that particular Hb molecule can no longer be used to transport oxygen. And that effect lasts until the Hb molecule is regenerated in your body and replaced by a fresh Hb molecule. I think the average lifespan of an Hb molecule is around three-months, so it may that long to recover fully from a serious case of CO poisoning.
This is also the reason that putting someone on 100% oxygen doesn't help all that much in case of CO poisoning. It's not the lack of oxygen that's the problem, it's the lack of oxygen transport capability.
Carbon monoxide - Wikipedia, the free encyclopedia
Hemoglobin - Wikipedia, the free encyclopedia