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.

President Barack Obama, meanwhile, has said he wants Congress to vote on a pared-down version of a fiscal cliff deal, one most House Republicans would surely not support.

Either way, the House will be in session starting Sunday. Majority Leader Eric Cantor, R-Va., told members on the conference call that votes are expected at 6:30 p.m. on Sunday and the House may be in session through Wednesday Jan. 2, just a day before the 113th Congress resumes.

The rare post-holiday weekend session sets up what could be a last ditch effort to pass a plan to avert the fiscal cliff, and it means Congress could very well be in session on Monday, which is New Year’s Eve.

It remains unclear what Congress will vote on, but Boehner reiterated to his members what he Cantor, Majority Whip Kevin McCarthy, R-Calif., and Conference Chairwoman-elect Cathy McMorris Rodgers, R-Wash., said in a statement Wednesday.

“The House has acted on two bills that collectively would avert the entire fiscal cliff. We passed HR 8 at the beginning of August to stop all of the tax rate increases that are set to occur on Jan. 1 under current law. And we’ve passed legislation to replace the entire sequester with responsible spending cuts,” Boehner said according to a source on the call. “These bills await action by the Senate. And as I, Eric, Kevin and Cathy said yesterday in a joint statement: If the Senate will not approve these bills and send them to the president to be signed into law in their current form, they must be amended and returned to the House. Once this has occurred, the House will then consider whether to accept the bills as amended, or to send them back to the Senate with additional amendments. The House will take this action on whatever the Senate can pass — but the Senate must act.”

But the speaker’s hand has been weakened after his conference rejected his call to pass a “plan B” — and the bruises in the conference are still showing. Rep. Tom Cole, R-Okla., expressed his support for the speaker and said that the conference had let him down. Other expressed their support for leadership as well. “We didn’t have a failure of leadership, we had a failure of followership,” Cole said on the call.

In a sign of just how charged and hyperbolic this year-end debate has become, House Minority Whip Steny H. Hoyer, D-Md., used an unfortunately timed comparison that likened Republicans trying to use the debt limit for leverage on spending cuts to people threatening to shoot their own children.

“It is somewhat like taking your child hostage and saying to somebody else, ‘I’m going to shoot my child unless you do what I want done.’ You don’t want to shoot your child,” Hoyer said at a press conference following a brief 10-minute pro forma session for the House.

Hoyer expressed serious frustration over the House’s continued holiday recess without any resolution to either the fiscal cliff or a laundry list of issues still awaiting congressional approval, from the extensions of the Violence Against Women Act and a foreign intelligence bill to farm legislation to a disaster aid supplemental and a postal overhaul bill.

Democrats on both sides of the aisle have used the recess to attack Republicans for being lackadaisical about a packed year-end agenda. Senate Majority Leader Harry Reid, D-Nev., said earlier Thursday that he couldn’t see a way to pass a budget agreement in the time left on the calendar.

Amid the pessimism over the fiscal cliff, Vice President Joseph R. Biden Jr. swore-in Sen.-designate Brian Schatz, D-Hawaii, to replace the late Daniel K. Inouye.

Reid had called for a hastened replacement process in case Democrats needed an additional vote to approve any year-end deals.