21st Century Fox execs had better pray that CBS crushes Time Warner Cable in their now week-long program carriage contract dispute. If CBS can’t win a fat increase in the fee that TWC pays to carry the network-owned stations, Showtime, and other channels, then Fox’s day-long effort Thursday to rally Wall Street’s support for its stock could look like a waste of time. Fox’s business plan is based on its faith that pay TV providers — and perhaps their customers — will keep paying rising amounts for a bundle of channels.  “People will give up food and a roof over their head before they give up television,” Fox COO Chase Carey told analysts and investors. Fox will take advantage of that addiction by creating new pay TV channels, raising prices for existing ones, and demanding higher payments for its Fox broadcast stations.

Turns out that’s the only way Fox execs can fulfill their promise to increase revenues by high single digit annual rates, up from the recent average of 5% a year. Ad sales won’t do it. The company says they’ll grow at low to mid-single digit annual rates. Content sales, expected to rise by low single digits each year, also won’t help hit the target. Instead the company must raise pay TV affiliate and subscription fees by low teen percentages each year. By 2016 “over half of [Fox’s] revenue will come from affiliate/subscription sources,” up from about 44% now, Bernstein Research analyst Todd Juenger concludes. Fox says the money’s all but in the bank: It has deals in place to cover 90% of the pay TV distribution fees it will collect for 2014, 70% for 2015, and 55% for 2016. Will that be Fox’s last gasp as the pay TV bundle implodes — the victim of growing demands for a la carte pricing, or cord cutting, or if new services such Aereo win the right to offer broadcast TV without paying retransmission fees? Carey continues to talk tough. It’s a “fantasy,” he said, to think that distributors soon will offer channels a la carte. Cord cutting is “not an immediate threat.” And Aereo’s just a “gimmick.”

Wall Street analysts loved the swagger. Lazard Capital Markets’ Barton Crockett raised his target price for Fox shares by $4 to $42. Wells Fargo’s Marci Ryvicker took her range up to as much as $41 from her previous high of $36. Credit Suisse’s Michael Senno moved to $38 from $34. And RBC Capital Markets’ David Bank went to $37 from $32.

But investors should consider how quickly the new conventional wisdom about Fox could sour. Financially strapped consumers may disprove Carey’s assumptions about cord-cutting. Aereo might prevail in court, giving cable operators additional leverage to resist broadcaster demands for high retransmission fees. Liberty Media’s John Malone could engineer a big cable merger. Or satellite providers DirecTV and Dish Network might beat him to the punch and decide to combine — a possibility that both companies now talk about openly. Cable and satellite execs agree that they need the scale to help them fight back when companies such as Fox demand higher prices. Then again, Time Warner Cable may just surprise the Street — and Fox — by showing that it’s already big enough to force CBS to accept far less than it wants.