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But when the conversation moves away from abortion to contraceptives - as it has this week - the intensity gap flips: A much larger segment of voters are willing to penalize a legislator who votes to defund family planning. That became apparent in polling that Democratic firm Lake Research Partners did earlier this year, which found that 40 percent of voters would be less likely to support a member of Congress who votes to defund family-planning programs. Just 22 percent would be more likely to support such a lawmaker.

That particular poll isn’t a perfect analogy for the current debate about the contraception mandate. But it speaks to something I’ve heard a lot in recent interviews with abortion right supporters: When the reproductive health debate moves away from abortion, it becomes easier to message and connect with voters. Unlike abortion rights, an issue that tends to split voters, most polls on contraceptives and birth control tend to find Americans solidly in support. That Lake Research poll I mentioned earlier found that 84 percent of Americans view family planning, including contraceptives, as basic health care.

Why White House sees political opportunity in the contraception battle - The Washington Post

I’d say this also makes it easier to bring up the fact that the anti-choice crowd is largely anti-sex and anti-women. And that if they get Roe overturned, they’ll go after Griswold v. Connecticut next.