WASHINGTON — Among the sticking points standing in the way of a final deal on what could be the first significant bipartisan gun safety legislation in decades is an age-old question: How do you define a boyfriend?

The question may sound frivolous, but for a small group of Republicans and Democrats who are pressing to translate a hard-won compromise on guns into legislation that can draw 60 votes in the Senate, it is vital. And for millions of women who have been threatened with a firearm by an intimate partner, it is deadly serious.

At issue is a provision in the proposed agreement that would make it more difficult for domestic abusers to obtain guns.

Current law bars people convicted of domestic violence or subject to a domestic violence restraining order from being able to buy a gun, but it applies only if they have been married to or lived with the victim, or had a child with them. Lawmakers have worked unsuccessfully for years to close what has come to be known as the “boyfriend loophole” by expanding the law to include other intimate partners. Taking such a step is seen as one of the more publicly popular and effective ways to reduce gun violence.

But first, lawmakers must agree on what exactly makes someone an intimate partner. Is it one date or several? Could an ex-boyfriend count?

Senator Christopher S. Murphy, the Connecticut Democrat who has been leading the talks, described it as “a complicated question of state statutes and state charging practices.”

Senator John Thune of South Dakota, the No. 2 Republican, said the boyfriend question was surprisingly complex.

“The surface explanation seems like it would be fairly simple, but I know that as they try to reduce it to legislative text, I think it’s gotten a little bit more uncomfortable,” said Mr. Thune, who is not directly involved in the negotiations.

Lawmakers are racing to finalize the legislation and pass it before the Senate’s upcoming Fourth of July recess, which would require at least 10 Republican senators to join Democrats to break a Republican filibuster.

The agreement on new gun legislation includes enhanced background checks for prospective gun purchasers under the age of 21, which would for the first time allow law enforcement to examine juvenile and mental health records. It would provide federal money for states with so-called red flag laws that allow the authorities to temporarily seize firearms from people deemed to be dangerous. The compromise also is expected to toughen laws to stop gun trafficking and include money to shore up mental health resources in communities and schools, as well as for school security.

The final haggling has centered on the details of closing the boyfriend loophole, including the definition and whether those subject to the gun ban should be able to appeal. Negotiators also spent Thursday debating the red flag law funding and whether states that do not have such laws can receive money.

The impasse on the boyfriend loophole has become so sticky that Senator John Cornyn, Republican of Texas and a crucial player in the talks, said the proposal could be dropped from the package altogether.

“We’re not ready to release any smoke, so we don’t have a deal yet,” Mr. Cornyn said, declaring “I’m not frustrated — I’m just done” as he left a private negotiating session that stretched into the afternoon on Thursday.

Republicans want to limit the reach of the domestic violence provision, while Democrats want to write it broadly.

“There are many people who committed domestic violence who aren’t actually charged with domestic violence — they are charged with simple assault, but they unquestionably committed an act of domestic violence,” Mr. Murphy said, adding, “We are at a pretty critical stage of the negotiation, and so I’m not going to share anything that jeopardizes our ability to land this.”

The inclusion of the boyfriend provision in the bipartisan framework, which was released on Sunday with the backing of 10 Republicans and 10 Democrats, was one of the biggest surprises for officials in both parties, given the repeated failed attempts to address it in the past. Earlier this year, lawmakers were forced to drop a similar provision from an updated version of the Violence Against Women Act — a landmark law intended to stop domestic violence, stalking and sexual assault — because Republicans objected.

“This is the difference between doing what sounds good and actually saving lives,” Representative Cori Bush, Democrat of Missouri, said of closing the boyfriend loophole. “We understand that we can’t get everything, but we have to do enough when we can see the research is there.”

That research, as well as analysis from leading gun safety organizations, shows that millions of women have been threatened with a gun by an intimate partner. Between 1980 and 2008, more than two-thirds of people killed by a spouse or former spouse were shot. Several of the gunmen involved in mass shootings in recent years, including at the Pulse nightclub in Orlando, Fla., in 2016 and a church in Sutherland Springs, Texas, in 2017, had histories of domestic or familial abuse.

As talks began over a compromise on gun safety legislation in the aftermath of devastating mass shootings in Buffalo, N.Y., and Uvalde, Texas, Senator Kyrsten Sinema, Democrat of Arizona, led the push to address domestic violence as part of the framework, aides involved with the discussions said.

But an agreement on the details of the provision has proved elusive, even as the lead negotiators — Ms. Sinema, Mr. Cornyn, Mr. Murphy and Senator Thom Tillis, Republican of North Carolina — have huddled repeatedly in hopes of a breakthrough that could allow votes on the legislation next week.

Other senators have raised questions about whether the provision should be retroactive, or whether someone barred from purchasing a gun under the measure, particularly because of a misdemeanor, should have an opportunity to appeal — and how long they must wait before they can do so.

“A lot of our members, as you know, are always concerned about making sure that there is robust due process built into some of those provisions, and so I think that’ll be really key on that one,” Mr. Thune said.

The proposal under discussion, like many of the elements of the agreement, is narrower than what Democrats have pushed for in the past, including in a bill introduced by Senator Amy Klobuchar of Minnesota. In a floor speech this week, Ms. Klobuchar signaled that she, like other Democrats, would support the legislation even if it fell short of her original plan and other gun safety proposals.

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