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Santa delivered sacks stuffed with IOUs this Christmas.

Across the country, carriers failed to meet delivery deadlines in the face of bad weather and an unexpectedly large surge in demand.

“It is unfortunate for this to happen at this time of year, but we’re working around the clock to fix it,” said Natalie Black, a spokeswoman for UPS Inc. “We had our peak projections, and the volume has exceeded our projection.”

“We are sorry,” she continued.

Although the scope of the problems was unclear, Walmart, the country’s largest retailer, apologized for late deliveries. Walmart and Amazon were among retailers that said they would give gift cards to customers who did not receive items in time.

UPS, the world’s largest package delivery company, attributed the late arrivals to a short holiday shopping season, a rise in online shopping and bad weather, including ice storms last weekend that caused power failures from Michigan to Maine. Together, they overwhelmed UPS’ air network.

Black said only a small percentage of parcels scheduled to arrive Christmas Eve were delayed, but she declined to provide a number.

FedEx also appeared to be experiencing delays. A FedEx spokesman told the Associated Press that some customers were able to pick up delayed packages at FedEx Express centers on Wednesday. FedEx did not return calls to comment.

Customers took to social media to complain as they bemoaned having to offer apologies instead of presents, some of which were ordered well in advance.

Rachel Shelton, a consultant for MBA applicants who lives in Connecticut, ordered gifts from Kohls.com for her mother almost two weeks ago, and her tracking information from UPS and Kohls indicated that the items would arrive on Christmas Eve. Tuesday, one box arrived, but only one item was inside.

Shelton called UPS customer service four times, but she was disconnected.

“The fact that my mom didn’t get her pajamas isn’t going to scar anyone for life,” Shelton said. “But when kids don’t get their presents from Santa, that breaks my heart.”

Black, of UPS, said the company had projected that it would process 132 million deliveries last week but declined to detail the extent of the excess demand.

Black said that most of the remaining parcels should be delivered today or Friday.

But on Christmas Day, some customers did not appear to be much interested in explanations.

“UPS is the Grinch of Christmas,” David Erdman tweeted.