An overwhelming proportion of Americans oppose rolling back Roe v. Wade, the landmark 1973 Supreme Court decision that guarantees a woman’s right to an abortion, according to a new poll from the Kaiser Family Foundation.

The poll — which was conducted prior to the announcement of Justice Anthony Kennedy’s retirement — found that about two-thirds of Americans do not think Roe v. Wade should be overturned, with roughly the same percentage of men and women expressing this viewpoint. The results are a bit more stratified along party lines, with 81 percent of Democrats agreeing that the decision should stay intact, while just 43 percent of Republicans do.

The preservation of Roe v. Wade has been chief among the concerns that Democrats have expressed following the announcement of Kennedy’s departure, a move that is expected to shift the court further to the right.

As Vox’s Dylan Matthews writes, Kennedy’s decision to step down means the court will likely have the votes to chisel away at the protections offered by Roe — or even overturn the decision wholesale.

Although he’s a conservative, Kennedy was a pivotal swing vote on the high court — siding with liberals on numerous abortion cases, including Planned Parenthood v. Casey, which reaffirmed Roe in 1992. More recently, Kennedy also voted with the Democrats in favor of striking down Texas regulations on abortion clinics.

Undoing Roe is not that simple, of course. Here’s Matthews’s breakdown:

This may take years after the replacement’s confirmation; a state would need to pass a law clearly incompatible with the Court’s existing approach to abortion rights and wait for the challenge to reach the Supreme Court before the new justice would have a chance to join a ruling. The anti-abortion movement might choose a more cautious strategy, instead chipping away at Roe with measures that fall short of outright bans.

As University of Florida law professor Nancy Dowd tells Vox, public sentiment is one unknown that could play a role in drumming up opposition to such efforts — or at the very least, slowing them down. “One unknown to add to the mix is the response of women, who are most deeply affected,” she says. “Even women opposed to abortion find the existence of the right important to them in particular circumstances, or would afford this to women who feel differently.”

Democratic senators are already trying to appeal to the potent attachment people have to abortion rights as one means of pushing a Kennedy replacement who’s closer to the center, according to Politico.

If two-thirds of voters see this as an issue at the polls, it’s possible lawmakers could think twice about backing a candidate who intends to launch an outright attack on the decision.