Watch: the Democrats next move...
Possible scenario: GOP gets Roe v Wade overturned (or at least thrown back to states)...Dem's win back Presidency with radical Hillary or Dean type (1% possibility). Dem President refuses to acknowledge the overturned Roe v Wade.
History: They've learned (and lost).
Yeah, and? States that want to regulate and restrict abortion will do so, and punish violations of the law, and there'd be nothing the President could do about it.
Overturning Roe v Wade wouldn't place any demands on the President or Congress, so there'd be nothing for them to ignore. It would simply mean the Court is no longer taking a stance on the issue. Congress could choose to pass legislation legalizing abortion in all States, at which point the Court could rule on that legislation, but it would be a matter entirely separate from Roe v Wade.