Jeff Cormier and his Dallas family were among those who ordered gifts that didn't arrive.
He had three separate UPS packages — including two for which he paid extra for expedited shipping — delayed.
"I've had to apologize to three different people when I thought I had everything wrapped up and good to go way before," Cormier said.
He and his wife are celebrating their baby daughter's first Christmas and flew in his grandmother from Ohio to join them. Her gift, a customized iPhone cover with a photo of her new great-granddaughter, didn't come in time for Christmas.
"My wife and I had our presents to open. Our daughter had her presents to open. And my grandma, she didn't have anything to open," Cormier said.
"We apologize that our customers did not receive their packages on Christmas," said Natalie Godwin, a spokeswoman for United Parcel Service Inc.
Godwin said snow and ice in the Midwest last week and an ice storm that hit Dallas two-and-a-half weeks ago were partially to blame. She also said the volume of packages shipped exceeded the capacity of UPS but would not share the number of packages shipped or what the company's maximum capacity is.
UPS did not make pickups or deliveries Wednesday. Extra workers were being brought in Wednesday night to the company's hub in Louisville, Ky., to sort packages for Thursday and Friday delivery, according to Godwin.
Godwin said "UPS will honor its peak shipments commitments" to customers who used its air delivery service. Those shipping by ground have no guarantee past Dec. 11. Godwin said she didn't know if customers would receive refunds.
However, some FedEx customers are able to pick up packages Christmas Day at their local FedEx Express centers.
"We're sorry that there could be delays and we're contacting affected customers who have shipments available for pickup," said Scott Fiedler, a spokesman for FedEx Corp.
Between Thanksgiving and Christmas, FedEx handled 275 million shipments, according to Fiedler. Those that were not delivered in time, he said, "would be very few."
Three people told The Associated Press that when they tracked their packages online, FedEx said deliveries to their homes were attempted but failed because "the business was closed." During follow-up calls with customer service, they said they learned that the local depot was overwhelmed and didn't attempt delivery.
On Sunday, Eric Swanson ordered a doll for his daughter and a sweater for his wife through Amazon.com and one of its affiliated sites. As an Amazon Prime customer, there was a promise of two-day delivery, getting the gifts to his Carmichael, Calif. home just in time for Christmas. One was shipped via UPS, the other FedEx.
"I thought it would happen," Swanson said. Online tracking tools said the packages would arrive by 8 p.m. Tuesday. Neither did.
Amazon.com has been notifying some customers affected by the UPS delays that it will refund any shipping charges and is giving them a $20 credit toward a future purchase.
Amazon spokeswoman Mary Osako said the company processed orders and got them to its shippers "on time for holiday delivery" and is now "reviewing the performance of the delivery carriers."