A 20-week abortion ban has finally passed the House, four months later than expected. It has already produced alarm about its supposedly dire consequences, but the conventional wisdom is that the bill will be killed in the Senate. Democrats will likely vote against the bill in lockstep, and the Republican majority alone cannot overcome a filibuster—much less a veto.

This frustrates the will of a huge moderate majority of Americans who support the ban. While pro-life and pro-choice extremists have problems with the bill, the Washington Post found that 64 percent of Americans support restricting abortion beyond 20 weeks. Women are more likely to support such a ban than men, and younger people more than older people. With support for the ban politically popular, GOP presidential candidates are going on offense, almost gleefully pushing their pro-choice opponents to defend wildly unpopular late-term abortions.

Despite this support, the bill seems unlikely to pass. The GOP has every incentive to allow the bill to fail in the Senate because, when it does, it will have a familiar pitch to offer National Right to Life, the Susan B. Anthony List, and other pro-life groups: “Please, just support our candidates against the moderate Democrats who voted against the bill for 2016, and we promise to bring it up again after we have more members in the Senate.” Pro-life groups will once again work to get Republicans elected, will once again be successful, and then party leadership will once again continue to pay only lip-service to even moderate pieces of legislation. After all, their small government hearts—and their strong anti-government tea-party caucus—struggle to justify the kind of federal government necessary to regulate abortion.

The U.S. political discourse on abortion seems unable to shake the hopelessly simplistic binary between life and choice of the 1970s and 80s. The “you’re either for it or against it” approach is problematic in American politics more generally, but it does particular violence to the views of most Americans about abortion. A majority of Americans claim the term “pro-choice” describes them somewhat or very well while simultaneously claiming that the term “pro-life” describes them somewhat or very well. Given this complexity, perhaps it is not surprising to find that 61 percent of Americans believe that abortion should be broadly legal during the first trimester—while only 27 percent support the choice during the second.

As if the lazy binary isn’t bad enough, the political maneuvering of the major parties around the abortion debate has been nothing short of bizarre. It has led Democrats and Republicans to take positions on abortion in line with something that I call the “Costanza Strategy.” Fans of Seinfeld will remember the hilarious episode where George “does the opposite” of every instinct he’s ever had and it turns out great for him. On abortion, the two parties also seem to exhibit the opposite of their usual political instincts. Republicans claim to be skeptical of big government and push for the autonomy and freedom of individuals to make private decisions. Except when it comes to abortion. Democrats want government’s protection for the voiceless and marginalized over and against the autonomy and freedom of those who have power over the vulnerable. Except when it comes to abortion.

Unsurprisingly, the Costanza strategy is a relatively new approach for the parties, which until recently exhibited a much broader array of views on the subject of abortion. When he was governor of California, Ronald Reagan signed the law permitting abortion in that state. As a national Republican candidate though, he somehow became a hero of the pro-life movement. He also appointed George H.W. Bush as his running mate, another Republican with a pro-choice record. When the elder Bush ran for president, he too switched to become pro-life. The former pro-choice governor of Massachusetts, Mitt Romney, also shifted away from his pro-choice position for his own run at national politics. Similar shifts took place with Democrats: Party leaders such as Ted Kennedy, Jimmy Carter, Al Gore, Joe Biden, Jesse Jackson and Bill Clinton all expressed views that were strongly skeptical of abortion—until the Costanza strategy kicked in. Then, like their Republican counterparts, they were forced to get in line with the new abortion orthodoxy.

And, to this point at least, the parties have been given no incentive to do anything differently. Quite the contrary, in fact: The parties have a strong interest in the status quo. Consider Juan Williams’ argument that both Republicans and Democrats benefit from keeping the abortion conversation locked in failure. It is one of the best wedge issues for producing money and for motivating their electoral bases. This is why the same fixed pattern of debate with the same prescribed divisions recurs over and over again, election-cycle after election-cycle. The Costanza strategy works, despite its incoherence, because it keeps the current arrangements of political power safe for those who benefit from them.

Ordinary voters, though, are less divided on the issue of abortion than their elected representatives. A 2011 Gallup poll found that 27 percent of Democratic voters were pro-life, with 44 percent claiming that abortion should be legal in “few or no circumstances.” This while 28 percent of Republicans are pro-choice, with 63 percent claiming that some abortions should remain legal in some form.

As recently as 2009 a full quarter of the Democrat caucus was pro-life. So what happened to all these pro-life Democrats? The GOP singled them out for defeat in the 2010 midterms and, using the money and ground-game of pro-life groups, devastated their ranks. Given the disappointing record of the GOP in enacting even moderate pro-life legislation, it is difficult to see how such groups could be happy with their investment.

But the coming Senate debate on the 20-week ban presents the perfect opportunity for the moderate middle on abortion to press both parties to act. Does the GOP really care about protecting prenatal children?  If so, it should be prepared to compromise to get the bill enacted. Can it find language with respect to the victims of sexual violence that will be acceptable to moderates on both sides of the aisle? What creative additions to the bill could get moderate Democrats on board? Adding a policy like mandatory paid-maternity leave to the bill would be a good place to start.

This is the right thing to do for women and families, period. It is a proposal that pro-lifers who are not beholden to the Republican party have been pushing for some time now. But it is also the kind of game-changing political move that could swing enough Democrats to create a veto-proof majority. A 20-week ban is truly moderate legislation. Most European countries have restrictions at 13 weeks and below. If the bill offers the chance to finally enshrine a civil right for women in law, reasonable Democrats will be all but forced to resist the abortion orthodoxy enforced by pro-choice groups like NARAL and Emily’s List.

The result of this compromise, perhaps something like the Mother and Pain-Capable Child Protection Act, would be a victory for women, babies, and common sense in abortion politics. Senator Lindsey Graham, sponsor of the Senate bill, is a Republican who has been known to make a deal or two for the good of the country. Why can’t his staff meet with the staff of a moderate Democrat like Claire McCaskill to make this deal happen? Their conversations, though lagging far behind those of the American people, would signal a new and hopeful moment in the abortion debate. And that is long overdue.