The House will return for votes on Sunday, but Speaker John A. Boehner assured his conference that he is not interested in putting a fiscal cliff measure on the floor that would pass with more Democratic votes than Republican.

On the packed GOP members-only call, Rep. Duncan Hunter, R-Calif., asked Boehner, R-Ohio, whether he would allow Democrats to carry a bill if the Senate passed a bill to which most House Republicans would object.

“I’m not interested in that,” Boehner remarked, according to a source on the call.

The speaker’s intention to stay steadfast means a rocky final stretch before Congress plummets off the fiscal cliff. Senate Majority Leader Harry Reid of Nevada tried to put pressure right back on Boehner by asking him to take up the bill the Senate passed earlier this year that extends the 2001 and 2003 tax rates on the first $250,000 of American’s annual income.

Reid and Senate Minority Leader Mitch McConnell, R-Ky., argued on the floor Thursday afternoon over the procedure for the Senate-passed bill, showing that at least publicly, the two leaders are not close to each other’s positions. McConnell said the Senate-passed bill was a “glorified sense of the Senate” that was going nowhere because, as a revenue measure, it did not originate in the House, per the Constitution.