NEW YORK (CNNMoney) -- We've heard the threat before: your favorite shows are being held hostage. This time, the dispute is between Time Warner Cable and CBS.

Time Warner Cable claims that CBS is demanding a big rate hike for cable customers in major cities. The cable giant says the fees will amount to 600% more than customers in other parts of the country will pay.

If the two companies do not soon come to an agreement about the fees, CBS could block Time Warner Cable customers from watching the channel and hit shows like "Under the Dome." The deadline is 5 p.m. Wednesday, according to several news reports.

Cable companies and satellite providers typically pay broadcasters "retransmission fees" in order to air the network's programming. It's not always the national networks like CBS, Fox, Disney's ABC and Comcast's NBC, that Time Warner Cable must negotiate with -- the cable provider has to agree to terms with all the various local affiliate stations to carry the national networks' content in each metropolitan area, many of which are owned by companies other than the big broadcasters.

That's where the latest round of deal-making is getting held up: CBS is currently negotiating on behalf of the several local affiliate networks it owns outright, and Time Warner Cable argues that CBS is demanding fees that are much larger than the fees it pays to other independent local stations that carry CBS shows.

Customers in New York, Los Angeles, Dalals, Boston, Pittsburgh, Chicago, Detroit and Denver could be affected, according to Time Warner Cable. But customers in other areas of the country are not in jeopardy of losing the CBS channel.

Neither Time Warner Cable nor CBS could immediately be reached for comment.

CBS is running TV commercials warning customers of the negotiations and that "Time Warner Cable is threatening to hold your favorite shows hostage."

"CBS is working in good faith to resolve this situation, but wants to alert you that Time Warner Cable may disrupt your TV viewing as early as next week," it says.