Speaker John A. Boehner and GOP leaders are considering throwing some red meat onto the House floor in the coming weeks as frustration mounts from members who are tired of sitting idle while high-level fiscal cliff negotiations continue between the Ohio Republican and the White House.

Boehner’s warning Wednesday that members should be ready to stay through Christmas to deal with any fiscal cliff measure has set off a round of griping from Republicans who already think that if they must be on Capitol Hill, they should at least have a proactive agenda.

As a result, leadership is considering bringing back to the floor a bill to replace the scheduled 10-year, $1.2 trillion sequestration cuts to defense and social programs — a bill that already passed earlier this year.

The lame-duck floor schedule has been conspicuously light, with Majority Leader Eric Cantor, R-Va., scheduling low-wattage votes this week as Boehner and President Barack Obama trade fiscal cliff offers behind closed doors — keeping even other members of the GOP leadership in the dark.

“There is a little pushback on that. I think the members would rather this be an open debate,” Rep. John Fleming of Louisiana said Wednesday. “We’re voting on one bill today. The whole day we’re voting on one bill. On the rule. We voted on the journal last night. I mean, it’s comical. It really is. And it’s sad. Because we’re not in regular order. All the work’s being done behind the scenes by staff and then the speaker and the president.”

GOP Conference Chairwoman-elect Cathy McMorris Rodgers of Washington said the sequester bill would help put the public’s focus back on the defense cuts, rather than revenue-raisers and the extension of tax rates that Obama wants to talk about.

Similarly, Rep. Tom Cole of Oklahoma, a member of the GOP whip team, said the sequester has been underused as a means of leverage by the GOP, so bringing it to the fore again would be beneficial to the party.

“Our leverage in this debate is not taxes, it’s not the 98 percent, it’s the spending,” he said. “Democrats don’t want to lose the domestic spending, and, honestly, I don’t think any commander in chief would want to look at the defense cuts we’re seeing.”

Some members, however, are looking for more. Outgoing Republican Study Committee Chairman Jim Jordan of Ohio said he and others have encouraged GOP leaders to bring to the floor a package that includes not only the sequester replacement but also another extension of the 2001 and 2003 tax rates.

“We’ve talked to some folks about putting together the package we voted on this summer. I think that makes sense,” he said. “It’s been suggested several times, so we’ll see.”

The idea was brought up most recently in a Wednesday morning conference meeting and again in an afternoon meeting of the RSC.

In the RSC meeting, Rep. John Culberson of Texas proposed bringing up the fiscal cliff plan offered by Obama with $1.6 trillion in tax increases for a House floor vote, expecting it to lose by a large margin. But Rep. Reid Ribble of Wisconsin later said he was cautious about that, thinking Democrats will vote for it.

GOP members and aides, however, said bringing messaging bills to the floor while such sensitive negotiations continue could poison the talks between the president and the speaker.

“It could be distracting,” Cole said. “We’re at the point where you either trust your negotiator or you don’t, and I think most people trust the speaker.”

Outgoing Conference Chairman Jeb Hensarling of Texas said a lame-duck session is not the time to be passing bills on the floor of the House, particularly not now when the focus is on the fiscal cliff.

Another argument, propagated even by those who want to take some action, is that floor votes on fiscal cliff topics would not move the public opinion needle when the president has such a formidable bully pulpit.

Even Fleming said the legislation would have no effect in the larger narrative.

“I’d rather have something on the floor, but the problem is, we’ve done it on the floor and to keep just repeating … that just so we can wave it in front of a camera to alter American opinion I just don’t think works,” he said.

Still, the prospects for those who want floor action do not look good. The rule that Congress passed Wednesday gives House leaders the authority to bring suspension bills to the floor anytime through Dec. 28, not just the regular Monday through Wednesday schedule. That could leave the floor full of several more low-priority bills. GOP leaders have held back on contentious bills, such as the farm bill and the Violence Against Women Act, which have split the Republican Party. A spokesman for Cantor said he will announce next week’s floor schedule during colloquy Thursday.

With talks seemingly moving in slow motion, Hill sources said a deal would need to be reached by Dec. 16 to ensure lawmakers could go home for Christmas. If lawmakers do not find a deal in principle in the coming days, there likely would not be enough time to put the agreement in legislative language, vet it and pass it in both chambers before Dec. 25.

Of course, the less significant the deal, the more swiftly it could be approved. Lawmakers have been speaking for weeks about a two-part process to deal with the wide range of spending and revenue issues facing them. If the first part of that agreement, for example, is just the House taking up an already-approved tax bill passed by the Senate to extend tax breaks to 98 percent of Americans, politicians could get home quickly.

The deadline pressure could start forcing the sides to move together, but sources in both parties and chambers seemed resigned Wednesday to the notion that they will break for two days at most for the holiday and then return for the remainder of December.

Meredith Shiner contributed to this report.