The argument I’ve heard is the words “liberty and pursuit of happiness” in the constitution which is the grounds for gay marriage and everything else under the sun including abortion.
The freedom to live your life as you choose is an important protection that the Constitution was meant to protect, with the understanding that your decisions did not impact others in a way that was unfair or unjust. Many of our civil rights, including those which protect gays, are codified into law (or added as amendments) because they were not clearly delineated in the Constitution. Gay marriage has been left to the states to decide, in the same way that abortion will be now. That is how it works, ideally.
To me, the issue around abortion is the fact that you are ending a life, and that should never be done lightly. If there is a question of the life/safety of the mother, that strikes me as the one thing that would be a clear priority. The issues of body autonomy and circumstances of the pregnancy should be secondary to that. We should first consider that to kill a baby that is viable is effectively murder, or I'd want to hear a good reason that it would not be. We can work our way back from there, but that should be the start point: do we value human life, or don't we?