If the Court indeed holds that the Constitution doesn't protect abortion rights, the debate will move to state legislation (as well as to state constitutional decisionmaking). And I expect that some of that legislation will be through the initiative and referendum process.
My sense from the surveys is that there is a good deal of support even in many majority-Republican states for protecting abortion rights at least in the first trimester—and that in some of them, the voters are more pro-abortion-rights than the state Legislature. Such mismatches between statewide public sentiment and results in the Legislature often do happen, for a variety of reasons; nor do they necessarily reflect anything nefarious: Different modes of legislation aggregate public preferences in different ways. But in any event, such mismatches are a classic example of where initiatives and referenda can make a difference (as we've seen, for instance, with anti-race-preferences initiatives in various states).
To give just one example, consider Utah. The Legislature there recently banned abortions with exceptions for rape, incest, and the woman's health. But the public appears closely divided on abortion rights generally, with one poll reporting that 47% of Utahns say abortion should be legal in most or all cases, and 51% say it should be illegal—doubtless within the margin of error, and potentially within the margin of political compromise and perhaps political persuasion.
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