House Republicans say they feel little political pressure to pass a bipartisan unemployment benefits extension expected to pass the Senate in the coming days, bolstering Speaker John A. Boehner’s hand as he holds out for concessions from Democrats and the White House.

Sen. Dean Heller, R-Nev., who helped negotiate the bipartisan Senate agreement, said once the his chamber clears the bill, he plans to reach out to House Republican leaders.

“I knew that [House Republicans] would have some issues with it,” Heller said. “It sounds like they want to get something done, in general terms. … Whether it looks like what the Senate passes or not, that is for them to decide.”

Senate Majority Leader Harry Reid, D-Nev., said he plans to bring up the bipartisan benefits extension bill soon, although a final vote could slip into next week.

House Democrats say they will keep pushing once the Senate passes the bill, a Democratic aide said. They plan to work with outside groups to target vulnerable Republican House members in hopes that they will convince Boehner to take up the bill, if only for their political benefit.

“It’s been tough to put pressure on House Republicans while the Senate is still negotiating an agreement,” the aide said. “Once that passes, it’ll be a lot easier to turn up the pressure.”

The problem, however, is that there may not be enough politically vulnerable Republican members who are feeling significant electoral pressure in their districts. Many Republicans simply do not believe long-term unemployment insurance benefits should be extended, and others aren’t convinced the Senate package is the way to go.

“It will encourage unemployment,” said GOP Rep. Devin Nunes of California, which has one of the highest unemployment rates in the country. “We see the need to have unemployment [benefits], no question. But to extend this … I just don’t see how we have the votes.”

So far, Boehner has been cool to the Senate’s proposal. The Ohio Republican told reporters on Tuesday that he would rather see the Senate take up House-passed proposals he believes would create jobs, and cited concerns from the National Association of State Workforce Agencies that the Senate bill would be difficult to implement.

“Let’s just wait and see what happens here,” Boehner said of Senate action. “I’ve made clear what I thought was necessary for us to pass it, those criteria have not been met and those criteria have not changed.”

Labor Secretary Thomas E. Perez tried to allay those concerns last week, saying that the implementation issues could be worked out. But for the time being, it has given Boehner and his conference a reason not to act on the bill.

For the most part, Boehner’s conference has followed his lead. Nevada has the second-highest unemployment rate in the country, well above the national average. Rep. Joe Heck, R-Nev., signed a letter to in December along with six other House Republicans calling on Boehner to act on a benefits extension bill. Yet on Tuesday, he said he shares Boehner’s concerns with the Senate’s bill.

“The Senate’s move to do something may have wound up with something that’s not usable,” he said. “We don’t want to pass something just for the sake of passing it if it’s not going to have any impact on those it’s meant to help.”

Similarly, Rep. Peter T. King, R-N.Y., who also signed the December letter, said he supported the idea of extending unemployment insurance, but with the legislation in its current form, he said he “could see why the speaker isn’t going to bring it up as is.”

He said he is not afraid of Democrats using the issue as an election-year bludgeon. “It’s like an issue a week for them I think,” King said.

Meanwhile, potentially electorally vulnerable House Republicans such as Rep. Steve Southerland II, R-Fla., echoed that sentiment, noting that they are feeling little to no pressure in their districts to move the bill.

“I was back in the district last week for 10 days and I did not have one person, in 14 counties, mention that issue to me,” Southerland said.

Freshman Rep. Rodney Davis, R-Ill., who is also facing a competitive re-election fight, said he received no feedback from constituents during the district workweek on extending unemployment insurance unless Davis himself brought up the subject.

But Davis signaled that he would be amenable to passing an unemployment insurance extension provided it includes other provisions, for instance, helping out-of-work Americans get job training.

Rep. Scott Rigell, R-Va., who represents a district that narrowly voted for President Barack Obama in 2012, said he’s not worried either.

Rigell said the offset in the Senate bill — a combination of revenue-raisers, including extending customs user fees — is “deficient,” but that he is still considering the bill.

Adding to the problem is a short House calendar. The House recesses for two weeks staring April 11 and the Senate bill would only extend the benefits through May, though it would cover benefits retroactively to December.

Matt Fuller, Emma Dumain and Humberto Sanchez contributed to this report.