Amazon is trying to set new standards in customer choice and fast delivery in its battle with online rivals. Nearly four in 10 online shoppers say they now expect retailers to offer free two-day delivery. About half of millennials expect it, making "fast and free" the new norm. Under pressure from increased demand, Amazon recently asked small businesses to help them complete the "last leg" of delivering packages.

"Amazon has surging demand. It has not stopped in this race to give us faster, better, cheaper at our doorstep. It's really taking the supermarket and the mall and bring it to us, if you think about it," said Leigh Gallagher, Fortune magazine's senior editor at large. "That is enormously complicated, and it's really maxed out Amazon's ability to use partners like the USPS, DHL, UPS, FedEx. It's using them all to the max."

Amazon Prime van Lindsey Wasson / REUTERS

Amazon is offering to help entrepreneurs start and manage a delivery business with potential $10,000 reimbursements for some candidates and vehicle leases.

Gallagher said Amazon is "so focused on the consumer, it just spends and spends and spends."

"Not every company can do that," she said. "But it's raised the bar, so everyone has to keep up."

Other large retail companies are also trying to compete, including Kroger, which is investing in automated warehouses and driverless cars, and Target.

"Target has partnered with a company called Shipt to offer same-day service and same-day delivery, among other things, so it's all about faster, faster, faster," Gallagher said. "It's never been a better time to be a consumer. You can sit at home and have everything come to you."

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