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NEW YORK (CBS NEWS) – Are UPS and FedEx having trouble meeting record demand this holiday season? According to a story in The Wall Street Journal, package volumes “have blown past expectations.”

While both package delivery giants deny that’s the case, they’re bracing for a spike in traffic following today’s Free Shipping Day, with more than 1,000 online merchants allowing customers to get free shipping and delivery by Christmas Eve.

Millions of orders made since Thanksgiving have already arrived even as the world’s two largest packages deliverers suspended the delivery guarantee, according to the Journal, which cited statistics from software developer ShipMatrix.

In an email to CBS MoneyWatch, UPS spokeswoman Susan Rosenberg said the ShipMatrix data was based on a small sample that lead to erroneous conclusions about its performance.

“There have been a few locations where volume surged beyond expectations for that site, or weather caused some delay,” she wrote. “But UPS has expertly flexed resources and personnel to manage those issues, the same as we do every year to shift personnel from other UPS sites or the Corporate HQ to address spot needs.”

FedEx also denied any holiday service problems.

“FedEx is proud to have achieved outstanding service during the first several weeks of the peak holiday shipping season,” wrote spokeswoman Katie Wassmer in an email. “We prepare year round to be able to meet the surge in demand, and will continue to work closely with our large retail and e-tail customers during these final weeks leading up to Christmas to ensure our networks are prepared to continue to deliver the holiday.”

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