Retailers are promising to deliver more packages in just a day, an attractive feature for shopping procrastinators like Jeff Chin.

“Some people plan ahead, but some might not—like myself,” said Mr. Chin, a physician in the San Francisco Bay Area. “You think of someone to get a gift for last minute, and if it comes the next day, it’s that much easier.”

The scramble between Thanksgiving and Christmas, already a hypercompetitive period for retailers, has gained a new twist, as the nation’s largest companies lure shoppers with faster delivery offers. Pushing the delivery needle is Amazon . com Inc., which is spending $1.5 billion in the fourth quarter to expand its free one-day shipping program.

“We’re adding new transportation capacity and putting more selection in fulfillment centers closer to customers,” said Maria Renz, Amazon’s vice president of global delivery experience. Customers say they continue to look for quicker delivery options, even if they are planning ahead for the holidays.

While many traditional retailers are struggling to keep pace, Walmart Inc. and Target Corp. have held their ground by increasing their delivery capabilities or getting shoppers to pick up online orders at their stores. Both chains reported strong third-quarter digital sales and increasing foot traffic.