If they do not reach a new deal by Thursday, CBS would go dark in markets like Los Angeles and New York, depriving viewers of summer shows such as "Under the Dome" and "Big Brother."
This would add to the challenges that cable companies and traditional broadcasters already face from competitors such as Netflix that are making inroads with viewers who can opt to watch shows online instead of paying for cable subscriptions.
Netflix said on Monday that it had added 630,000 U.S. streaming video customers in the second quarter of this year.
Cable companies have not yet released quarterly financial results but the top nine cable operators lost about 264,000 video subscribers in the first quarter, according to Bruce Leichtman, president of Leichtman Research Group, which tracks cable and broadband subscribers.
In TV commercials airing in some U.S. markets, Time Warner Cable accuses CBS of giving New York a "black eye" while CBS tells consumers in its own spot to "say no to Time Warner Cable."
"Anytime you have arguments that result in blackouts, that is negative for the industry," said Gabelli & Co analyst Brett Harriss. "It's negative for both CBS and Time Warner Cable."
CBS and Time Warner Cable will eventually settle, as cable operators and media companies always do out of necessity. Cable operators need someone to cover the hefty cost of making TV shows they air and media companies like CBS need the fees they get from cable companies.
Consumers being bombarded by the marketing campaign know how it will end: they will pay higher subscriber rates to the cable operator to carry CBS.
"It's not smart to be rubbing consumers' noses in how much we pay for something, especially if it's something that could go away," said Wedbush Securities analyst Michael Pachter.
The industry is mature and not growing. Today, there are 100 million customers paying for television subscriptions through cable, satellite and telecom companies, according to cable research firm SNL Kagan. That number has been about flat since 2011.
Craig Moffett, an analyst at Moffett Research, estimates that about 2 million households have cut the cord, or cancelled their video cable service, since 2010.
CBS is also facing challenges to its business model. It is suing Aereo, the Internet TV service backed by veteran media executive Barry Diller, for not paying for its broadcast signal. It is also in court against satellite operator Dish Network, whose Hopper digital video recorder automatically skips over commercials.
CBS Chief Executive Leslie Moonves, a former actor, is one of the media business' toughest negotiators and is playing hardball with Time Warner Cable.
"If on Thursday our content has been pulled off their service, you'll know that we are in the midst of a crucial struggle we intend to bring to a satisfactory conclusion," he told CBS staffers in a memo.
Time Warner had already encouraged viewers to subscribe to Aereo to access CBS and other channels for a fee of $8 a month, none of which goes to CBS.
"Is it really a good idea to intentionally drive customers to Aereo? What if they liked it too much?" Moffett said.
TV viewers are already all too familiar with blackouts. Last year alone, there were 91 blackouts, up from 51 in 2011 and 12 the year before, according to the American Television Alliance, which tracks these disputes.
While there is no evidence that blackouts encourage TV viewers to cancel cable subscriptions, there are hints of the damage that can be caused by a blackout of channels. Last summer, satellite operator DirecTV said its churn, or rate of cancellations, increased when Viacom's networks including Nickelodeon and MTV went dark for 10 days.
Christina Wong, a 31-year-old Los Angeles resident who works in public relations, said she dropped her cable subscription five years ago and blackouts are among the reasons she would not renew it.
"Hearing about all these fights is just bad publicity," said Wong. "If that was something I'd be paying for, I'd be very angry."
(Reporting by Liana B. Baker; Editing by Ron Grover, Toni Reinhold)
By Liana B. Baker