ALBANY ⁠— Progressives are hoping Gov. Andrew M. Cuomo will sign a bill that would make it harder to disqualify votes cast as affidavit ballots, a change they say could greatly impact the Democratic primary for district attorney in Queens, where a controversy over the legitimacy of thousands of paper ballots is playing out.

Affidavit ballots are filled when someone shows up at the polls but cannot be found in the voter rolls. It is not uncommon for most to be invalidated, either because the person is not registered to vote or they are registered with the wrong party, election attorneys say.

The measure, which passed the Legislature this session but has not yet been sent to Cuomo, was first sponsored in the wake of a drawn-out 2012 Senate race in the Capital Region that sparked similar demands for a recount and allegations of foul play.

Tuesday's primary ended with public defender Tiffany Cabán, a progressive firebrand supported by U.S. Rep. Alexandria Ocasio-Cortez, holding a lead of more than 1,000 votes over Queens Borough President Melinda Katz, the choice of the local party establishment.

But after absentee ballots were counted Wednesday night, Katz claimed a narrow advantage of roughly 20 votes.

The Working Families Party, which supports Cabán, is pressing lawmakers to move the bill, which they say would open up some of the invalidated affidavits.

"In Queens right now, voters that everyone agrees are eligible to vote are being disenfranchised because poll workers failed to tell them how to fill out a form correctly," WFP director Bill Lipton said.

He called on Assembly Speaker Carl Heastie to send the bill to Cuomo's desk. Heastie's spokesman was not available for comment Friday.

Bills that are passed by both houses of the Legislature are sent to the governor's desk by the house in which the bill originates — in this case, the Assembly.

Since the mid-1970s, it has been the practice to ship bills to the Executive Chamber throughout the year, even after the formal legislative session has ended. In most cases, the governor's office lets each house know when it's ready to consider a bill. Once a measure is sent over, the governor has 10 days to sign or veto it; if he takes no action, it becomes law.

The pending legislation was initially introduced by former Democratic state Sen. Cecilia Tkaczyk in 2013 after she beat out Republican George Amedore by 18 votes following a lengthy, court-supervised recount of hundreds of absentee and affidavit ballots.

Tkaczyk, a sheep farmer from Duanesburg who was unseated by Amedore two years later, gained 54 votes as election commissioners opened 90 ballots held by county boards of elections, undoing Amedore's initial lead. The 74-day delay prevented Tkaczyk from joining the Senate Democrats at a time when she could have provided a tie-breaking 32nd vote.

In Queens, Katz has declared victory — but more than 2,000 affidavit votes invalidated by the borough's Board of Elections are in dispute by her opponent's camp.

"We know that these numbers can and will be subject to recount, and there may be legal challenges," Katz said in a statement, "but what matters most is the will of Queens voters. Not the interest groups, not the donors from outside our community and not even the candidates. This is democracy."

Approximately two-thirds of the affidavit ballots were disqualified due to voter registration issues, but at least a hundred have been dismissed for having been filled out incorrectly.

Cabán's campaign is claiming that at least 20 registered Democrats were invalidated by the Queens Board of Elections for failing to write "Democrat" on their form, a deficiency they say the bill would have addressed.

Tkaczyk's bill, now carried by Queens Democratic Sen. Leroy Comrie, would eliminate a requirement for voters to list a prior address and would soften the standard for election officials to accept affidavit ballots.

Under the bill's provisions, forms would only have to "substantially comply" with requirements to be counted.