Last week, former Vice President Joe Biden withdrew his support of the Hyde Amendment, which prohibits coverage of abortions under federal health care programs for poor people. Many progressives see Biden’s reversal as a sign of “an emerging consensus within the Democratic Party.” “There is #NoMiddleGround on women’s rights,” says Sen. Bernie Sanders. “Under my Medicare for All plan, we will repeal the Hyde Amendment.” On Sunday, Sen. Kirsten Gillibrand made the same pledge. “I don’t think there is room in our party,” said Gillibrand, “for a Democratic candidate who does not support women’s full reproductive freedom.”

It’s true that Biden’s moderate record on abortion and other issues—he has supported legal abortion but also some restrictions—has made him a target of the party’s progressive wing. But it’s not true that opposition to the Hyde Amendment has become broadly popular or a consensus position among Democrats. Surveys taken in the past three years debunk much of what the left believes, not just about public support for government-funded abortions but also about how attitudes on that issue intersect with gender, class, and reproductive freedom.

In every poll, a plurality of Americans opposes public funding of abortions. In every poll but one, that plurality is a majority. The questions vary, but the result is the same. Respondents support “banning federal funding for abortion” except in rape cases or to save the woman’s life (Politico/Morning Consult, 2019). They believe that “government health insurance programs for low-income women, like Medicaid,” should not “cover abortion” (PRRI, 2018). They oppose “using tax dollars to pay for a woman’s abortion” (Marist, 2019). They oppose allowing “Medicaid funds to be used to pay for abortions” (Politico/Harvard, 2016). When they’re told that “the Hyde Amendment prohibits federal funds from being used to fund abortions, except in the case of incest, rape or to save the life of the mother,” they endorse the amendment (YouGov, 2016). These polls aren’t close. The average gap between the pro-funding and anti-funding positions is 19 percentage points.

Self-identified Democrats support federal abortion funding, but the margins are narrow. In a 2017 Marist poll, Democrats favored the use of tax dollars for abortions by 8 percentage points. In the Morning Consult poll, which was taken last weekend, they opposed the Hyde Amendment by 6 points. In the YouGov poll, they opposed the ban by just 3 points. A pro-funding position, on balance, probably does more to hurt the candidate in a general election than to help in a Democratic primary.

To many advocates of abortion rights, covering the cost of an abortion like any other medical procedure is a matter of respecting women. But in surveys, women are no more likely than men to support that policy. The sexes differ on other reproductive policy questions, but not on abortion funding. Consider a poll taken two months ago for the Kaiser Family Foundation. On federal funding of “family planning and birth control for lower-income women,” the gap between men’s and women’s answers was about 10 to 20 percentage points. On funding of Planned Parenthood clinics that provide “birth control, STD testing and treatment, and cancer screenings,” the gap was similar. But on funding clinics that “also provide abortions” or that “also provide referrals for abortions,” the gender gap disappeared. The Harvard poll found the same pattern: Women were more likely than men to support funding of Planned Parenthood, but not more likely to support Medicaid coverage of abortions.

Why would the gender gap on reproductive health care dissolve when the question turns to abortion? Apparently, something about abortion bothers a lot of women in a way that birth control and STD treatments don’t.

It’s also common on the left to hear that opposition to abortion, including opposition to Medicaid coverage of abortions, is driven by hostility to sex or to women’s autonomy. But polls show an enormous gap between support for funding abortions and support for funding contraception. In the PRRI survey, only 46 percent of respondents agreed that “government health insurance programs for low-income women” should “cover abortion.” But when the same question was asked with one substitution—the phrase “cover the cost of birth control” replaced the phrase “cover abortion”—support jumped to 83 percent. Even 75 percent of Republicans endorsed covering birth control.

Likewise, in the KFF poll, 76 percent of respondents said it was important “that the federal government provides funding for reproductive health services, such as family planning and birth control for lower-income women.” Coverage of reproductive health care is popular. But coverage of abortion isn’t.

A lot of people seem to think that the right to choose abortion is compatible with the right not to pay for other people’s abortions.

In announcing his reversal, Biden said the government should guarantee women not just the legal right to abortion, but also the financial means to “exercise their constitutionally protected right.” That’s a prevalent view on the left: If you don’t support abortion funding, you’re not really pro-choice. But nearly half of pro-choicers disagree. In the 2016 and 2017 Marist polls, 40 percent of respondents who identified themselves as pro-choice rather than pro-life also opposed “using tax dollars to pay for a woman’s abortion.” In the YouGov poll, 66 percent of respondents said “the decision on abortion should be made by a woman and her doctor,” but 55 percent supported prohibiting federal funding of abortions, again showing a large overlap. A lot of people seem to think that the right to choose abortion is compatible with the right not to pay for other people’s abortions.

Many opponents of the Hyde Amendment see it as a class issue. That’s how a Biden adviser made the case in pressing the former vice president to change his position. But there’s little evidence that people of limited means see it that way. In the 2017 Marist poll, among people with annual incomes of $50,000 or more, the margin of opposition to tax-funded abortions was 16 percentage points. Among people who earned less than $50,000, the margin of opposition was 32 points. In the YouGov poll, respondents with lower incomes were less likely than respondents with higher incomes to support federal and state funding of abortions. And in the Harvard poll, support for Medicaid funding of abortion was almost twice as high among voters who earned more than $75,000 as among voters who earned $25,000 or less.

How will Biden’s switch play out? The Morning Consult poll, taken in the three days after his reversal, projected a net gain among Democrats: 30 percent said his decision made them more likely to vote for him, while 19 percent said it made them less likely. But among voters as a whole, the poll found a net loss in both absolute numbers (24 percent less likely to support Biden, 19 percent more likely) and intensity (16 percent much less likely, 7 percent much more likely). Among men, women, and people in every income category, the effect of the switch was, on balance, negative.

If you’re a supporter of abortion coverage for poor women, these numbers may depress you. But there’s a constructive lesson: Direct payments for abortion, which are outlawed by the Hyde Amendment, are the least popular way to help women end their pregnancies. People are much more willing to involve public mandates and resources in the provision of abortion when tax dollars don’t specifically go to that procedure.

In the Harvard poll, by a 22-point margin, likely voters opposed “allow[ing] Medicaid funds to be used to pay for abortions.” But by a 21-point margin, they also opposed “ending all federal funding to Planned Parenthood because they provide some abortion services.” The question about Planned Parenthood split Republicans, and even Trump voters, right down the middle. In the KFF survey, 60 percent of respondents opposed “prohibiting federal funding for reproductive health and preventive care services from going to clinics that also provide abortions, even though none of the funds could be used for abortions.” And in a Marist poll taken last week, most voters endorsed “a law that requires insurance companies to cover abortion procedures.”

On the core question of the abortion debate, most Americans agree with the Democratic Party. They believe that women, not the government, should make the decision. And they don’t support defunding clinics that provide abortions. But on the question of direct payments, most voters agree with the GOP. If Democrats make that question a litmus test, they’ll regret it.