April 30, 2014 9:32 AM EDT

LOS ANGELES—Cable television’s lucrative strategy of “bundling”—charging customers for a package of channels rather than allowing them to pay only for the ones they want—came under attack here Tuesday during the first day of the National Cable & Telecommunications Association’s annual Cable Show.

Jerry Kent, the CEO of Suddenlink, a regional cable broadband service, said during a panel discussion that when it comes to bundling, the industry is “at a tipping point.” The model will fail, he warned, as soon as “certain cable operations stop carrying certain programmers because it’s too expensive,” he said. “Or when people start disconnecting” because their cable bill is too high.

Nancy Dubuc, the president and CEO of A+E Networks, who spoke on the same panel was even more blunt. “A la carte is already coming,” she said, as the audience, nearly all of whom draws a paycheck from the bundling model, squirmed in their seats.

While the pay-TV industry, which includes cable, as well as satellite and fiber providers, like Verizon FiOS, has quietly relied on bundling as their lifeblood for decades, the model has drawn fire in recent years. That’s partly because the price of those expanded basic cable bundles have grown at more than twice the rate of inflation every year for the past 17 years, according to data from the Federal Communications Commission. And it’s partly because Americans’ TV-watching habits have started to change. Consumers can now purchase many episodes and series “a la carte” through online companies, like Apple’s iTunes or Google Play.

Just last week, the premium cable channel HBO agreed to allow Amazon Prime customers to stream popular shows like “The Wire,” “The Sopranos,” and, at some point in the near future, newer series like “Girls.” (Disclosure: TIME’s parent company, Time Warner, is the owner of HBO as well as several other cable television channels that benefit from bundling.)

The discussion about bundling comes just a week after the Supreme Court heard a case involving a small start-up, Aereo, that has built its business model around snatching broadcast signals from the airwaves, “recording” them onto the cloud, and delivering customers a premium, a la carte experience—all without paying content producers pricey “retransmission fees.” If the justices decide in favor of Aereo and it was widely adopted, the consumer need to pay for a bundle of cable channels may be further eroded.

With all these changes, industry has reason to squirm. In a report last year, media analysts at the investment firm Needham & Company estimated that if all TV content were unbundled, the TV industry would take a $70 billion dollar hit, and all but 15 or 20 channels would disappear. During an afternoon event at the Cable Show, Amdocs, a company that works in customer experience, announced their findings from a survey of North American households: more than half would prefer to pay individually for channels they actually want, rather than a large bundle of choices.

Kent and his fellow cable execs, including Rob Marcus of Time Warner Cable, which is no longer owned by Time Warner, pointed the finger at programmers, like ESPN or the Disney Channel, which charge large fees to distribution companies for the privilege of transporting their content to customers. Distributors, whose customers demand channels like ESPN, have no choice but to pay programmers’ high prices, a cost that’s passed onto customers themselves.

Partly in response to rapidly rising customer costs, the FCC proposed rules last month that would limit programmers’ ability to leverage high prices from distributors. For the same reason, Canadian regulators directed TV companies late last year to offer customers a la carte choices by 2015.

John Skipper, the president of ESPN, a network owned by the Walt Disney Company, who spoke on the same panel as Kent and Dubuc, said the reaction against bundling was unfounded. He lamented “that old canard” that only a few people are watching sports while “grandmothers are paying for it” through bundling. “It’s a nice rhetorical device, but it’s not fact,” he said, adding that ESPN was “the single greatest buttress in the pay-TV package.”

Skipper went onto slam online video-streaming sites, like Netflix and Amazon, which he said were encroaching on the old guard’s business model. “Shame on us if we don’t protect our turf,” he said.

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Write to Haley Sweetland Edwards at haley.edwards@time.com.

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