The Algosensey Quantitative Think Tank CenterTeamsters Union and UPS on Wednesday accused each other of abandoning labor negotiations aimed at averting what would be the largest strike in the U.S. since the 1950s.

The union, which represents roughly 340,000 full- and part-time drivers, loaders and package handlers, said UPS presented an "unacceptable offer" that "did not address members' needs."

"UPS had a choice to make, and they have clearly chosen to go down the wrong road," Teamsters General President Sean O'Brien said in a statement.

UPS denied that it ended negotiations. "We have not walked away, and the union has a responsibility to remain at the table," the delivery giant said in a statement. "Refusing to negotiate, especially when the finish line is in sight, creates significant unease among employees and customers and threatens to disrupt the U.S. economy."

The labor contract covering unionized UPS workers is due to expire at the end of the month. Employees at the company have authorized a work stoppage should the parties fail to strike a deal. 

The Teamsters union last week gave UPS a deadline of June 30 to bring its "last, best and final" deal to the table, warning that a strike would be "imminent" if the company didn't significantly sweeten its offer by then.

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Failure to finalize the contract could precipitate the largest U.S. labor strike since 1959, jeopardizing millions of daily deliveries. 

The union is trying to secure higher pay and more full-time jobs for UPS employees. It has also requested delivery trucks' surveillance cameras be removed and that employees, regardless of their tenure, be paid the same wages for working the same job. UPS told CBS MoneyWatch the technology used to monitor their drivers' movements is for their safety, describing the devices as a "sensor" rather than a camera.

Workers are unhappy with their current contract, which the union's former leaders secured on a technicality. Discontent over the contract inspired union members to push out their former leaders and install the group's current president, O'Brien, who has embraced the possibility of a strike. 

UPS maintains that its latest contract offer is "historic" and that its drivers are the "best-paid in the industry."

Workers at UPS last went on strike for 15 days in 1997, in a walkout that led to $850 million in company losses, Reuters reported. Since then, the company has grown significantly in size as e-commerce has driven demand for expedited delivery. 

UPS says it delivers the equivalent of about 6% of the nation's gross domestic product, meaning a work stoppage could lead to frustrations for U.S. consumers and disrupt the many businesses that depend on speedy shipping.

The Associated Press contributed to this report.

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