When it overruled the governor and outlawed the death penalty in Nebraska on Wednesday, the state Legislature seemingly defied the polls. Around 60 percent of Americans support the death penalty for murder, and Republicans, who make up the majority of Nebraska’s legislators, favor it by an even wider margin.

So what happened?

The Nebraska Legislature has seemed intent on banning the death penalty for a long time. The Legislature failed to override a governor’s veto on the death penalty twice — once on a bill it passed outlawing the punishment in 1979 and again on a temporary moratorium in 1999. And in 2007, the Legislature came within a vote of approving a ban. This year, death penalty opponents won over Republican legislators with conservative arguments; Republican lawmakers said “they believed capital punishment was inefficient, expensive and out of place with their party’s values,” according to The New York Times.

And in that fact may lie hope for death penalty opponents nationally.

Polling has found that support for the death penalty drops when it’s difficult to execute people. According to a 2014 ABC News/Washington Post survey, the share of Americans favoring the death penalty falls from 61 percent to 48 percent when lethal injections are “outlawed or otherwise unavailable.” Nebraska has had a difficult time securing the drugs necessary to end a prisoner’s life by lethal injection. This complication became a big component of the death penalty debate in the state. It’s part of the reason that Nebraska hasn’t executed anyone since 1997. And many other states have had similar supply problems. This has contributed to a declining number of executions over the past 15 years.

It should also be said that national polling may overstate support for the death penalty. The death penalty wins majority support when polls ask about it in isolation, but not when life in prison without parole is given as an option. In an average of three live-interview polls from ABC News and The Washington Post, Gallup and the Public Religion Research Institute in 2014, only 45 percent of Americans favored the death penalty in cases of murder, compared with 48 percent who preferred life imprisonment without parole. This suggests that the death penalty majority isn’t all that firm.

In other words, a majority of Americans still favor the death penalty, but as Nebraska shows, that’s no guarantee that it will remain legal.