UPS and the Teamsters return to the bargaining table Tuesday, with one week to reach a new labor deal before the union’s strike deadline.

The International Brotherhood of Teamsters represents about 340,000 members at Sandy Springs-based UPS, making it the largest private collective bargaining agreement in North America.

A strike would disrupt millions of package deliveries, and has already prompted some companies to shift shipments to other carriers, including FedEx, to avert disruptions from a potential strike.

UPS said “we look forward to getting back to the negotiating table” and said it is “focused on reaching agreements that provide wins for our employees, the union, UPS and our customers.”

The Retail Industry Leaders Association last week issued a statement saying “the impact of a UPS worker strike would undoubtedly be felt throughout the economy, to the tune of billions of dollars” and urged a quick resolution in the negotiations.

“Reliable and quick shipping—ensuring the timely delivery of essential goods such as groceries, medicine, and school supplies to customers’ doorsteps—is the hallmark of our industry and the UPS fleet plays a critical role in that operation. Uncertainty is like kryptonite for supply chains,” the retail trade group said. “Retailers are preparing contingency plans, but even the most robust planning won’t shield retailers or consumers from the impact of shutting down a key component in the supply chain as we head full-steam into back-to-school and then holiday shopping seasons.”

Teamsters General President Sean O’Brien said on MSNBC on Sunday that “95% of the contract non-economic issues are done,” including a deal for UPS to equip new trucks with air conditioning. But contract talks broke down July 5 amid negotiations over economic issues, with O’Brien saying one of the sticking points was pay for part-timers.

On Saturday, O’Brien spoke at a Teamsters rally in Atlanta told members that part-timers “have been left behind.”

“UPS part-timers will be rewarded accordingly,” O’Brien said. UPS says its part-time union employees’ pay currently starts at $16.20 an hour, and they can work 3.5 hours or more each workday.

“I know people are scared,” he said. “I know that a potential labor strike could be devastating to the economy. But that’s not on us. That’s on UPS.”

“We’re almost there. We’re at that five-yard line,” O’Brien said. “We are in the fight of our lives.”