Sen. Richard Burr ( R-N.C.) at a hearing on Capitol Hill last month. (Jacquelyn Martin/AP)

A pair of Republican senators voiced considerable skepticism this week about the prospect of passing a bill to revamp the nation’s health-care laws in the coming months, injecting fresh uncertainty into the GOP effort to fulfill a signature campaign promise.

Sen. Richard Burr (R-N.C.) sounded a deeply pessimistic note when he told a local television station he believes it’s “unlikely that we will get a health-care deal.” Earlier in the week, Sen. Jeff Flake (R-Ariz.) said he doubted a bill could pass before the August recess.

The show of doubt in their home states during the one-week Memorial Day recess came as other Republican senators sought to temper expectations among constituents about how aggressively the Senate can go after the Affordable Care Act, known commonly as Obamacare.

With senators returning to Washington next week to resume work on health care, there are growing concerns among Republicans that political and policy differences among GOP senators could prevent a bill from ever winning passage.

“I don’t see a comprehensive health-care plan this year,” Burr told WXII 12 News on Thursday. Burr said he was “more interested in putting the American people back to work right now.”

Burr’s comments, which received widespread attention Friday, came on the heels of similar remarks by Flake.

“There are some still saying that we’ll vote before the August break. I have a hard time believing that,” Flake told members of the local Chamber of Commerce this week.

Sen. John Cornyn (R-Tex.), the chamber’s second-ranking Republican, expressed much more optimism that his GOP colleagues could work out their differences quickly and pass a bill.

“We’ll get it done by the end of July at the latest,” he told KFYO radio Wednesday.

Still, the serious challenges Republican senators face were clear as the recess wound down. For those determined to pass a bill, it’s not just a matter of ironing out the differences in policy; it’s also about convincing enough Republican senators that health care should be the party’s top priority right now and is worth the risk that the effort will end in failure.

“Most of them haven’t spent much time thinking about health care,” said Rep. Tom Cole (R-Okla.), who voted for a health-care bill that passed the House last month after its fate was in doubt for weeks. That bill headed over to the Senate. Cole said he believes some GOP senators “were sort of hoping at some level it wasn’t going their way. Well, it did.”

Senate Republicans are working on health care at a moment when multiple investigations into potential Russian meddling in the election, including possible coordination with Trump associates, are underway and occupying the attention of many GOP and Democratic lawmakers. The effort also comes amid a desire among some Republicans to proceed toward other sweeping goals, such as rewriting the nation’s tax laws.

Some Republicans say the Senate must act to undo parts of Obamacare after spending years campaigning on the promise of repealing the law. But even if they are able to pass a bill to do so in the Senate, it won’t be a total repeal as some hard-line opponents of the ACA would like to see — because of a procedural tactic congressional Republicans are using to try to pass it without having to count on any Democratic support.

Some Republicans have been forced to explain that strategy this week.

“What we have to do is find a way of repealing the pieces that we can and moving forward,” Sen. Joni Ernst (R-Iowa) said Tuesday at an event hosted by the Altoona Chamber of Commerce. “That just allows us to tinker around the edges. It doesn’t allow us to fully go in and repeal.”

Before senators left town last week, Cornyn said GOP staffers planned to have partial draft language of a bill ready for review. “I think people’s staff will start putting together some language we can look at when we return,” he said last week.

Some Republican aides familiar with the health-care effort, granted anonymity to speak candidly, expressed confidence that a bill could get done this summer, even though there are big potential roadblocks. As of Friday, several aides said, no concrete draft language of a bill had been presented to rank-and-file senators.

One said that an important gathering will be Tuesday’s weekly policy luncheon, when members will have a chance to exchange stories about what they heard from their constituents back home.

Other Republicans were less confident in Senate GOP leaders. One Republican in regular contact with senior members of Congress, speaking on the condition of anonymity, said they don’t seem to have a “real plan.”

Senate Republicans have mostly panned the House health-care measure, stressing that they are writing their own distinct bill. They are trying to resolve disagreements and come to an accord on a variety of issues, including how Medicaid should be structured and funded, whether to allow states to avoid certain ACA regulations and how to craft tax credits to replace existing insurance subsides.

The Senate cannot simply ignore the House bill, since GOP leaders are seeking to use the procedural tactic known as reconciliation that allows them to pass a bill with a simple majority. Otherwise, they would need to clear a 60-vote threshold, which would effectively doom any bill that seeks to undo parts of Obamacare. Republicans hold a narrow 52-to-48 majority in the Senate.

Senate aides are working with the nonpartisan Senate parliamentarian, who is charged with acting as Congress’s version of a referee in the contentious health-care debate, to see whether the House bill is consistent with Senate reconciliation rules — or whether any language must be struck from it.

Some Republicans, including Flake, have said that they would prefer working on health care on a bipartisan basis.

But no Democrats have expressed openness to supporting a repeal bill. They have said that only after Republicans drop their insistence on undoing major parts of the ACA would they be willing to talk about fixes that both sides can agree upon.

Ed O’Keefe in Glendale, Ariz., contributed to this report.