Anyone who has seen “On the Waterfront” knows East Coast longshoremen can be a tough bunch.

The dockworkers are flexing their muscles again, threatening a strike beginning Sunday that would shut seaports from Massachusetts to Texas. It would be the first such coastwide strike since a two-month walkout in 1977 paralyzed the flow of tens of billions of dollars of imports — and the nation’s retailers and other businesses fear a painful replay if the 14,500 dockworkers make good on their threats.

“Unless something miraculous happens, I think we’re looking at a strike,” said Kevin M. Burke, president of the American Apparel and Footwear Association, which represents an industry that imports $72 billion in dresses, shoes and other goods each year through the East Coast and Gulf Coast ports facing a possible shutdown.

“Our companies are preparing for the worst,” Mr. Burke said, “but hoping for the best.”

The strike threat has so alarmed corporate America that more than 100 business groups wrote to President Obama last week to urge him to intervene to push the two sides to settle — and, if need be, to invoke his emergency powers under the 1947 Taft-Hartley Act to bar a strike. President George W. Bush invoked the act in 2002 to end a lockout at ports on the West Coast, where a different union represents dockworkers.

Despite their small numbers, the East Coast dockworkers have outsize influence. Many of them, like the crane operators who transfer containers from ships to the docks, are highly skilled and cannot be easily replaced. And because they control the loading and unloading of goods in most of the nation’s ports, a strike could cause extensive economic damage at a time when the economy is already weak.