"I … expect the House to consider and pass a one-year debt limit increase," he said of the House's anticipated work next week.

"This increase will also contain a number of important pro-growth economic policies, healthcare and non-healthcare reforms, in addition to a one-year delay of ObamaCare."

Republicans have said the bill would include language aimed at approving the Keystone pipeline between Canada and the United States, a project the GOP says would create thousands of new jobs. As of early Friday afternoon, the House had not released a text of its debt ceiling bill.

Earlier today, the House passed a short-term government funding bill that would defund ObamaCare. Formally delaying the law as part of a debt ceiling bill is another angle of attack that could even be more effective than defunding, since much of the funding for the law is mandatory.

Cantor said the House would start work on Wednesday, but again noted that members may need to be in session the following weekend, depending on the status of spending resolution. The Senate is expected to try to strip the ObamaCare defunding language from the resolution and send it back to the House.

"The House will remain in session and potentially into the weekend until the completion of the continuing resolution," Cantor said. "The meeting time for a weekend session will be announced later next week."

Cantor spoke as part of his usual colloquy on the schedule with Minority Whip Steny Hoyer (D-Md.). This time, however, the colloquy was very short, as Hoyer yielded back after making a quick comment in the hopes that all of this work can be finished next week.

"I sincerely hope that we can reach a compromise next week," he said.