Santa delivered sacks stuffed with i.o.u.’s 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 United Parcel Service. “We had our peak projections, and the volume has exceeded our projection.”

“We are sorry,” she continued.

While 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.

U.P.S., 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 U.P.S.’s air network.