With the Teamsters contract set to expire Aug. 1, pay for part-time workers is a major hurdle. A walkout could rattle the U.S. economy.Barely a week before the contract for more than 325,000 United Parcel Service workers expires, union and company negotiators have yet to reach an agreement to avert a strike that could knock the American economy off stride.UPS and the union, the International Brotherhood of Teamsters, have resolved a variety of thorny issues, including heat safety and forced overtime. But they remain stalemated on pay for part-time workers, who account for more than half the union’s workers at UPS.A strike, which could come as soon as Aug. 1, could have significant consequences for the company, the e-commerce industry and the supply chain.UPS handles about one-quarter of the tens of millions of packages that are shipped daily in the United States, according to the Pitney Bowes Parcel Shipping Index. Experts have said competitors lack the scale to seamlessly replace that lost capacity.The Teamsters have cited the risks its members took to help generate the company’s strong pandemic-era performance as a reason that they deserve large raises. UPS’s adjusted net income rose more than 70 percent between 2019 and last year, to over $11 billion.The contract talks broke down on July 5 in vituperation. The two sides are to resume negotiations in the coming days, but the window for an agreement before the current five-year contract expires is tight.In a Facebook post this month, the union said the company’s latest offer would have “left behind” many part-timers, whose jobs include sorting packages and loading trucks. The post said part-timers earned “near-minimum wage in many parts of the country.”UPS, which says it relies heavily on part-timers to navigate bursts of activity over the course of a day and to ramp up its work force during busier months, said it had proposed significant wage increases before the talks broke down. According to the company, part-timers currently earn about $20 an hour on average after 30 days as well as paid time off, health care and pension benefits. The company noted that many part-timers graduated to jobs as full-time drivers, which pay $42 an hour on average after four years.The union has gone out of its way to highlight the challenges facing part-time workers. In television interviews and at rallies, the Teamsters president, Sean O’Brien, has emphasized what the union calls “part-time poverty” jobs. He has frequently been joined by leaders of other unions and politicians, including Representative Alexandria Ocasio-Cortez, the New York Democrat.UPS said Wednesday that it was “prepared to increase our industry-leading pay and benefits.” But it is unclear if the company will satisfy the union’s demands.“UPS certainly wants to reach an agreement, but not at the expense of its ability to compete long-term,” said Alan Amling, a former UPS executive and a fellow at the University of Tennessee’s Global Supply Chain Institute.Professor Amling estimated that it would cost the company $850 million per year to increase wages $5 an hour for all part-time employees represented by the Teamsters.The company, which normally reports its second-quarter earnings in late July, has delayed the report this year until after the strike deadline. UPS said that the timing was within the required window for reporting its earnings and that it had never published a date other than Aug. 8 for the coming release.The sometimes-volatile negotiations began in April, and the Teamsters announced in mid-June that their UPS members had voted, with a 97 percent majority, to authorize a strike.Less than two weeks later, the union said that it was walking away from the table over an “appalling counterproposal” from the company on raises and cost-of-living adjustments and that a strike “now appears inevitable.”The two sides resumed their discussions the week before the Fourth of July and soon resolved what was arguably their most contentious issue: a class of worker created under the existing contract.UPS said the arrangement was intended to allow workers to take on dual roles, like sorting packages some days and driving on other days — especially Saturdays — to keep up with growing demand for weekend delivery.UPS handles about one-quarter of the tens of millions of packages that are shipped daily in the United States.Maansi Srivastava/The New York TimesBut the Teamsters said that the hybrid idea hadn’t come to pass, and that in practice the new category of workers drove full time Tuesday through Saturday, only for less pay than other drivers. (The company said some employees did work under the hybrid arrangement.)Under the agreement reached this month, the lower-paid category would be eliminated and workers who drove Tuesday through Saturday would be converted to regular full-time drivers.That agreement also stipulated that no driver would be required to work an unscheduled sixth day in a week, which drivers had at times been forced to do to keep up with Saturday demand.Despite progress on these issues, Mr. O’Brien could face a delicate test persuading members to approve a deal if it falls short of the lofty expectations he helped set. He won the union’s top position in 2021 while regularly criticizing his immediate predecessor, James P. Hoffa, for being too accommodating toward employers.Mr. O’Brien argued that Mr. Hoffa had effectively forced UPS workers to accept a deeply flawed contract in 2018, even after they voted it down, and accused his rival in the race to succeed Mr. Hoffa of being reluctant to strike against the company.He began focusing members’ attention on the contract and a possible strike even before formally taking over as president in March last year, and has spoken in superlative terms about the union’s goals for a new contract.“This UPS agreement is going to be the defining moment in organized labor,” he told activists with Teamsters for a Democratic Union, a group that backed his candidacy, in a speech last fall.The union under Mr. O’Brien has held training sessions in recent months for strike captains and contract action team members, who rally co-workers to help pressure the company.And he has strongly urged the White House not to wade into the contract negotiation. In his Boston youth, “if two people had a disagreement, and you had nothing to do with it, you just kept walking,” he said during a recent webinar with members. “We echoed that to the White House on numerous occasions.” (Administration officials have said they are in touch with both sides.)In some ways the context for this year’s negotiations resembles the circumstances of the nationwide Teamsters strike at UPS in 1997. UPS was also in the midst of several profitable years, and the rapid growth in its part-time work force loomed large.Sean O’Brien, the Teamsters president, right, at the Los Angeles rally. He was elected in 2021 after criticizing his predecessor as having been too accommodating toward employers.Jenna Schoenefeld for The New York TimesBut while a reformist president, Ron Carey, had mobilized the union for a fight, its ranks appeared divided between his supporters and those of Mr. Hoffa, who had narrowly lost an election for the union’s presidency the year before. The union may have more leverage this time because its members appear far more unified under Mr. O’Brien.Barry Eidlin, a sociologist at McGill University in Montreal who studies labor and follows the Teamsters closely, said that while the ramp-up to the current contract fight had lagged in some parts of the country, where more conservative local officials are less enthusiastic, Mr. O’Brien had no serious opposition within the union.“Not everybody is a fan of O’Brien, but they’re not actively organizing to undermine him the way people were with Ron Carey in the ’90s,” Dr. Eidlin said. “It’s a huge, huge difference.”Still, for all his pugilistic statements, Mr. O’Brien remains an establishment figure who appears to prefer reaching a deal to going on strike, and he has subtly acted to make one less likely.Earlier in the negotiations, Mr. O’Brien had said that UPS employees wouldn’t work beyond Aug. 1 without a ratified contract, and that the two sides needed to reach a deal by July 5 to give members a chance to approve it in time. But last weekend he said UPS employees would continue working on Aug. 1 as long as the two sides had reached a tentative deal.“This isn’t a shift,” a Teamsters spokeswoman said Friday by email. “This is how you get a contract. Our pressure and deadline on UPS forced them to move in ways they hadn’t before.”Niraj Chokshi More