The American people believe in both abortion and capital punishment; they never see a disconnect.
You are right about being blind to the disconnect. I'd wager there are more pro-abortion folks who think capital punishment is wrong. Ironically, they see sucking the brains out of an innocent baby as perfectly fine, but think it's cruel to kill a criminal who has caused pain and fear as he committed some heinous crime against another human being.
I think they're suffering some form of insanity and it gets worse by being in contact with "free" stuff.