CBS believes the start of football will increase public pressure on Time Warner to get a deal. The network has run radio advertisements with football announcers like James Brown instructing affected fans on other ways to watch games.
"I'm not optimistic," said Jack Myers, an analyst whose Myers Report newsletter is widely followed in the television industry. "There have always been settlements in the past when they come up to big sports events. But this time, they're really playing it for keeps."
The talks are being closely followed beyond these companies and their customers because of the idea that a retransmission agreement will set a precedent for future negotiations between different networks and cable or satellite companies. Another sticking point is the cable operator's access to CBS material for on-demand or mobile device viewing.
(Read more: WhoseNFL jersey scores the most with women?)
Already, the dispute is a milestone "that may be cited as a turning point in the industry," said Robin Flynn, analyst for the financial research firm SNL Kagan.
The NFL's opening kickoff may not be as potent a pressure point as many people have assumed because of the way the schedule starts. CBS is not broadcasting any games involving New York or Dallas teams on the opening weekend; Los Angeles has no "home team" in the NFL. Dallas is playing the New York Giants on Sept. 8, but that's the Sunday night game on NBC.
CBS' first significant game for one of the local markets is on Sept. 15, when the Giants will face the Denver Broncos in a matchup featuring quarterback brothers Peyton and Eli Manning. The New York Jets first appear on the CBS schedule on Sept. 22, and the Cowboys not until Oct. 6.
(Read more: NFL, players to settle concussion suits: Judge)
"We are working hard to reach an agreement as soon as possible," said Maureen Huff, spokeswoman for Time Warner Cable. "But the negotiations or pace of negotiations are not tied to any game or event coming up."
On Friday, Time Warner began running a television ad telling customers that switching providers isn't a good idea. The ad says there have been some 200 blackouts due to business disputes in recent years, and that "even if you switch, you're still at risk for network blackouts."
Time Warner isn't saying how many customers it has lost because of the dispute, but Huff said the "vast majority" of customers who called inquiring about the situation have not switched.
After the blackout, CBS retaliated by blocking access to CBS programming online to people who get their Internet service from Time Warner, even people who are not cable customers. Huff estimated that affects more than 12 million people.
Time Warner has also blacked out the Showtime cable network for customers in the three cities (Showtime is a business partner of CBS). Showtime's most high profile show, "Homeland," begins a new season on Sept. 29.
The blackout affects roughly 1.1 million of New York's 7.4 million television households. In Los Angeles, an estimated 1.3 million of 5.6 million households are affected, and 400,000 of Dallas' 2.6 million TV homes.
CBS, which has had a strong summer behind its miniseries "Under the Dome," continues as the nation's most popular network. Its researchers estimate the blackout has cut CBS' national ratings by 1 percent. New episodes of the network's favorite prime time shows begin appearing in late September.
For both companies, though, the psychological impact is hard to measure. The longer the dispute goes on, the more customers who don't get CBS programming learn they can survive without it. Similarly, people who didn't think twice about signing up with an area's dominant cable provider are learning there are alternatives.
"The pressure is really on both sides to come to a resolution but both sides seem very adamant about holding on to their position," Myers said.