Unlikely. Remember that birds are dinosaurs... they spent a significant portion of their evolution at a time when there was a lot more CO2 in the atmosphere. Bird's lungs are much more efficient than mammalian lungs, which is why some birds can fly up to altitudes at which humans would lose consciousness if they weren't in a pressurized airplane cabin! With that and their mobility, birds (at least a few species) are good candidates for surviving the 6th great extinction... given that some are also very intelligent, maybe dinos will get another shot at inheriting the earth after all! ;-)