"The fact that we were only able to get 49 of 52 to support a proposal indicates there's still some disagreement," said Ohio Republican Rob Portman, referring to the vote count for the bill that failed last summer.
Key GOP swing votes, such as Sen. Lisa Murkowski of Alaska, say they would prefer to see the effect of the mandate repeal before a broader overhaul. Senate Majority Leader Mitch McConnell has also been pessimistic that any major health care overhaul could happen in 2018.
"Well, we obviously were unable to completely repeal and replace with a 52-48 Senate," the Kentucky Republican told NPR in December. "We'll have to take a look at what that looks like with a 51-49 Senate. But I think we'll probably move on to other issues."
Those comments do not appear to sit well with conservatives, who are ramping up pressure on Hill Republicans to tackle health care again this year.
"Americans need relief, and we believe they will hold their representatives accountable at the polls this November," representatives from 10 groups, along with former Pennsylvania GOP Sen. Rick Santorum, wrote in a recent letter to Trump and congressional leaders. "Health costs are rising faster than before, and there's no real prospect of a reversal without legislative action."
The letter cited a recent poll conducted by the Associated Press-NORC Center for Public Affairs Research, which found that health care remains a top issue for both Democrats and Republicans.
Senate Republicans might have an easier cycle than their Democratic counterparts in 2018. Only five GOP members are facing re-election this year, while three are retiring. But Alabama Democrat Doug Jones' arrival reduced the Republican majority to 51-49, and the minority party is more optimistic that control of the Senate is up for grabs.
"It's very clear what we want out of the health care system. It's something that actually results in lower prices, better quality of care. And we made that clear throughout the debate last summer and we're going to continue to make that clear," said Colorado Sen. Cory Gardner, the chairman of the National Republican Senatorial Committee.
Democratic political operatives say the proposals the GOP has presented to date will harm the party in the midterms.
"The problem for Republicans is that voters got a taste of their 'strategy' all year: higher health care premiums, an age tax and jeopardizing coverage for preexisting conditions. The GOP has worked to sabotage health care at every turn and that's why hardworking Americans will hold them accountable in November," said David Bergstein, a spokesman for the Democratic Senatorial Campaign Committee.