“One of the advantages of being the majority leader is you control the paper,” Mr. McConnell said, referring to legislation. “I wrote it in such a way that it does not prevent what is frequently done, which is the use of extraordinary measures. The minority leader and his team were trying to get us not to write it that way, but I did write it that way and that is the way it passed.”

Under the scenario Mr. McConnell sketched out, the December talks will now focus on hurricane relief and other budgetary matters and the administration can tell Democrats “see you next year on the debt ceiling.”

“I think I can safely say the debt ceiling and the spending issue in December will be decoupled because the debt ceiling will not come up until sometime in 2018,” he said.

The length of the increase in federal borrowing authority was a main sticking point in last week’s White House showdown that ended with Mr. Trump embracing the Democratic approach — his first real reach across the aisle on a major issue. Mr. McConnell and Speaker Paul D. Ryan were hoping for a much longer extension, possibly past next year’s election, and were caught off guard by the president’s acquiescence.

But though they are in the majority, Republicans need Democratic votes to raise the debt limit since many conservatives simply will not vote to do so. That dynamic is what caused Mr. Trump to accept the Democratic proffer.

Democrats were hoping that the same combination of factors — expiring federal funding and a necessary debt limit hike — would play to their advantage again in December, allowing them to cut an even bigger and more favorable deal that would cover spending for the rest of the fiscal year and other issues such as bipartisan legislation to stabilize health insurance markets and the immigration fight over young, undocumented immigrants brought to the country as children.