The 2nd amendment is explicit. Abortion is mentioned nowhere in the Constitution.
If you got 2/3 of congress and 2/3 of the States to mandate Catholicism and rescind the 1st amendment, that would happen. The question isn't of majority rule, it's the level of the majority required to make something law or constitutional.
I am mostly "on your side", but I see why abortion is different than almost any other situation. There is another life involved, regardless of what you or others think about the status of that lifeform.
To me 12 week limits on Birth Control abortions, (which covers rape and incest) followed by therapeutic abortions for the life of the mother, unless birthing the fetus after viability is an equal option. Miscarriages, stillborn, and non-viable fetuses are miscarriages, not abortions even if medically aided. Parental notification for minors having an abortion, No taking minors across state lines for abortions except by parents or guardians, and no government funds for birth control abortions (except rape, incest).