The programing fee dispute between the two sides is over how much the cable operator would pay Disney for the right to carry TV networks including ABC, various ESPN channels and other Disney-owned channels.
It affects several million homes across New York, Los Angeles, Houston, and other cities in Ohio, North Carolina and Florida.
Time Warner Cable spokeswoman Maureen Huff said both sides were still working on a deal and would have an update later in the morning.
Both sides had agreed on Sunday to cool off on a barrage of hard-hitting adverts aimed at customers and said they had made significant progress in what had become increasingly contentious talks.
While programing fee negotiations are always about how much the cable operator pays for carriage, the talks between Time Warner Cable and Disney were further complicated by issue such as competition from online video services.
Executives at Time Warner Cable had been concerned that reports of new services such as Apple Inc's 99-cent TV show rental service launched on Wednesday would compete with cable's offering.
The two sides also clashed over Time Warner Cable paying cash for a retransmission fee to carry free-to-air broadcast systems on their cable systems.
(Reporting by Yinka Adegoke; Editing by Michael Shields)