Speaker John A. Boehner’s decision to wait on the Senate before taking up a sequester replacement bill may be more tied to his own difficulties getting the votes for one than to a calculated political messaging strategy.

The Ohio Republican and other House leaders have repeatedly noted that the chamber passed two sequester substitutes last year, and they have used that fact to challenge the Senate to act. But the House has not yet approved any legislation in the new Congress to avert the more than $1 trillion in across-the-board spending cuts that will begin Friday.

The previous measures passed during the 112th Congress and would have to be passed again before the Senate could even consider taking them up. But even in the 112th Congress, both bills squeaked by with few votes to spare. That has led some sources to speculate that if the House brought up a similar bill again, it would quite simply fail.

“All the momentum in House Republican circles now is for keeping the sequester as is. I don’t see how any sequester replacement bill could get any oxygen for the foreseeable future,” one Republican aide said.

Indeed, many House Republicans have accepted the sequester as a reality, holding that it’s the only way to extract spending cuts from Democrats, no matter how bad the consequences back home in their districts.

Besides sequester replacement fatigue, however, House GOP leaders face a numbers problem.

Last year, the Sequester Replacement Reconciliation Act passed 218-199 in May with 16 Republicans voting against it. Then in December, the Spending Reduction Act passed by an even slimmer margin, 215-209, with 21 Republicans opposed. No Democrat supported either bill.

More than 30 Republican members who supported the bills are no longer serving in the House because of retirement, loss of election or running for another office. And in the 113th Congress, Republicans have eight fewer seats in the House.

All that leaves Republicans with the near-impossible task of whipping another sequester replacement bill that could pass without Democrats if they chose to bring it to the floor.

Still, in meetings with rank-and-file members and around the leadership table early in this Congress, House Republican leaders floated the idea of putting another such bill on the floor. What they found is that members had no appetite to vote on such a bill again, according to one GOP leadership aide.

“The conference feels that we’ve made our point by passing the sequester replacement act two times,” the aide said.

They will drill home that message this week as members make a concerted messaging push in news conferences and on the House floor that the Senate should act.

The Senate does plan to vote this week on both Democratic and Republican proposals to replace the sequester.

“If the president is going to grandstand on military bases and with first responders … House Republicans are going to counter that narrative with our own narrative: We’ve been trying to address this issue,” the leadership aide said.

The GOP’s Senate-first strategy, not just on the sequester but also on guns and other pieces of Obama’s agenda, has obvious benefits that Republicans have touted in recent weeks.

Primarily, the strategy could benefit them politically in 2014, when vulnerable Democratic senators might have to answer for votes they took on hot-button issues.

In that vein, the National Republican Senatorial Committee launched an online petition urging Senate Majority Leader Harry Reid of Nevada to “take the Obama challenge.” The petition mockingly criticizes Reid and Sen. Charles E. Schumer, D-N.Y., for continuing to “stonewall” Obama’s “liberal agenda.”

The strategy also aims to make Reid look ineffectual if he cannot pass the legislation.

But there are risks to the strategy, as well. Senate Republicans, with their own political interests, may vote for bills that aren’t palatable to House Republicans.

Two episodes from the last Congress — over payroll tax rates and the fiscal cliff — show the scenario is not so far-fetched. Both times, Senate Republicans largely backed bills that caused an uproar among House Republicans, forcing Boehner to do a delicate dance.

With even a handful of Senate Republicans on board, Democrats are instantly able to claim the mantle of bipartisanship, greatly increasing the pressure on the Republican- controlled House.

House conservatives are keeping a close eye on their Senate colleagues, with one House aide saying there is concern the sequester fight could turn into “fiscal cliff, part deux” if the Senate GOP sells out the House.

But the same source trusted Boehner not to flinch even if that were to take place.

GOP leadership aides, meanwhile, expressed their confidence in the coordination between House and Senate Republicans.

Boehner and Senate Minority Leader Mitch McConnell of Kentucky talk at least once a week. Their chiefs of staff meet frequently, and their communications teams meet every Friday.

One House GOP leadership aide said he had zero concern that Senate Republicans would agree to replace the sequester with even one dollar of tax increases.