Boxes of petitions for Initiative 594 at the Secretary of State’s office Wednesday, Oct. 9, 2013, in Olympia, Wash (AP photo/Elaine Thompson)

A ballot initiative that would require background checks on all firearm purchases in Washington state, including sales at gun shows and online, has support from a majority of voters — but that majority is shrinking.

A new survey conducted by The Elway Poll, a longtime Washington pollster, shows Initiative 594 earning 60 percent of the vote, while 32 percent of respondents say they will vote no. The initiative took 70 percent of the vote in July and 72 percent in an April poll conducted by the same company.

A rival ballot measure, Initiative 591, looks headed for a surer defeat. Just 39 percent of voters say they back that measure, which would prohibit the state from enforcing stricter background checks on gun purchases than are allowed at the federal level.

Pollster Stuart Elway said history argues that the pro-background check measure should have enough support to pass. Since 1992, 24 of 29 ballot measures that earned at least 60 percent of the vote in Elway’s September or October surveys have gone on to pass. But it’s not unheard of that support should drop sharply: In 2005, the state medical association and a trial lawyer interest group sponsored conflicting initiatives on medical malpractice awards; both scored better than 60 percent in the fall Elway Poll, and both lost in November.

The background check measure is passing among every demographic subgroup except Republicans, who say they will vote against it by 48 percent to 43 percent. But voters who are paying close attention to this year’s midterm elections — already more likely to be conservative — are much less likely to support I-594 than those who are only paying some attention or little to no attention.

Gun rights supporters began collecting signatures for their initiative, which would block the new background checks, in hopes of stopping the stricter law. But that approach opened a schism in the gun rights community: While the Second Amendment Foundation, based near Seattle, has worked to pass I-591, the National Rifle Association has kept its focus on defeating I-594, rather than advocating for I-591.

Some gun rights activists have questioned the level of the NRA’s involvement, and many point to a long-running feud between Alan Gottlieb, who runs the Second Amendment Foundation, and NRA leadership in D.C. The NRA has spent a total of $191,000 on the campaign, according to the Washington Public Disclosure Commission.

On the other side, supporters of tighter background checks have been running advertising both in favor of I-594 and against I-591. The pro-gun control campaign has vastly outspent gun rights backers, fueled by contributions from wealthy Washingtonians like Bill Gates, Paul Allen and Steve Ballmer, who have written several six-figure checks to the campaign.

The poll results suggest it is now unlikely that both measures would pass; in April, the Elway Poll showed I-591 passing with 55 percent of the vote. If they had both passed, the state would have faced its first-ever instance of conflicting ballot initiatives. There is no statute or court precedent to account for conflicting voter-approved laws in Washington, meaning the state Supreme Court would likely have been forced to weigh in.