Sen. John Thune (R-S.D.) addresses reporters on Dec. 18, 2012, on Capitol Hill in Washington. Thune, along with Senate Minority Leader Mitch McConnell (right) and John Barrasso (left) spoke on the ongoing “fiscal cliff” discussions. (Karen Bleier/AFP/Getty Images)

Republican leaders on Capitol Hill are scrambling to ease growing concerns among GOP lawmakers about rushing to repeal the federal health-care law before plans for a replacement take firmer shape, addressing complications to the effort to deliver on one of the party’s signature campaign promises.

In the Senate, where Republicans are using a budget package to move swiftly ahead with repeal, leaders are looking at ways to adjust their plans to address the skittishness that GOP senators have voiced in recent days.

The legislative crossroads highlights a key dilemma facing Republicans as they look to make good on their long-stated goal of shredding the law known as Obamacare: Although there is broad consensus in the party about doing away with the law, there is far less agreement about what a substitute should look like — or even how quickly one needs to be in place.

Sen. John Thune (R-S.D.), the third-ranking Senate Republican, told reporters Monday that GOP members of the House, Senate and the incoming administration are having ongoing conversations as they formulate a “path forward” for addressing the health-care law.

“I would fully expect that a repeal vote could be followed by several proposals, many of which our members have been trying to get voted on for years. You might see this thing in a very step-by-step way as opposed to having one huge 2,700-page bill,” Thune said.

President Obama and Vice President-elect Mike Pence each met with lawmakers from their parties, Jan. 4, to discuss plans for the Affordable Care Act. (Sarah Parnass/The Washington Post)

Republican senators concerned about not having a replacement plan ready when the law is repealed have come up with several different approaches to fix the process before the Senate votes this week on a bill that establishes a process for gutting President Obama’s signature health-care law. One proposal, released Monday, would buy the GOP more time to come up with a plan by giving lawmakers until March 3 to write the final repeal bill, rather than the Jan. 27 deadline in the legislation.

The amendment was introduced by Sens. Bob Corker (R-Tenn.), Rob Portman (R-Ohio), Susan Collins (R-Maine), Bill Cassidy (R-La.) and Lisa Murkowski (R-Alaska). Several of them have been outspoken about their reluctance to pursue repealing the law without having put forth plans for a replacement measure.

“I have great concerns that we inject a level of great uncertainty into an already uncertain environment if we don’t give people a clear indication as to what will come once we repeal,” Murkowski said Monday.

Murkowski also voiced concerns with Republican plans to defund Planned Parenthood as part of the budget package that has been designed to serve as a vehicle for moving ahead with repeal.

Republican leaders are relying on special budget procedures to repeal portions of the health-care law without the threat of a blockade by Senate Democrats.

Senate rules allow budget legislation to pass the Senate with a simple majority of 51 votes rather than the normal 60 needed to pass nearly everything else. There are 52 Republicans in the Senate, ensuring that a unified GOP can act on repeal without the help of Democrats.

But any new health-care legislation would be subject to normal Senate rules — meaning Republicans would need votes from at least eight Democrats to get the bill passed.

Donald Trump has campaigned to repeal and replace the Affordable Care Act, otherwise known as Obamacare, once he gets into office. Now that he's won the presidency with a majority Republican House and Senate, that feat might not prove to be too easy. Wonkblog's Max Ehrenfreund explains. (Daron Taylor/The Washington Post)

Some Republicans say they are satisfied with moving ahead on repeal in the budget resolution without replacing it in the same measure.

“I don’t think we need to see it in the same piece of legislation,” said. Sen. Joni Ernst (R-Iowa).

Still, Sen. Rand Paul (R-Ky.) said that in a conversation with President-elect Donald Trump last week, the two agreed on the need to immediately tackle replacement.

“He showed willingness and openness and was interested in getting a replacement that could be passed as part of repeal,” Paul said. “Now, we’re trying to get a bill out there this week.”

Meanwhile, several lawmakers have floated the idea of breaking up the replacement into a handful of smaller parts.

“We have to get the right sequencing on this,” said Sen. Lamar Alexander (R-Tenn.). “In my view we need to cast most of our votes on that before summertime. That will probably take two or three steps and then take two or three years to implement it over time.”

One option would be to break off some of the most politically difficult issues. Leaders could then tuck them into other must-pass legislation backed by Democrats, such as an authorization for parts of Medicare and the Childrens’ Health Insurance Program that is set to expire at the end of this year.

Another possibility would be to tie funding for some elements to a long-promised tax bill that Republicans hope to pass this year.

“We’re going to have comprehensive tax reform in the second reconciliation bill, seems the ideal to work all of that out,” Cassidy said.

Members of the tax-writing House Ways and Means and Senate Finance committees have been mulling tax restructuring proposals for several years. The topic was the subject of a lengthy closed-door meeting Monday between house Speaker Paul D. Ryan (R-Wis.) and several top Trump advisers.

Some, including Paul, have floated policies to resolve discrete issues within the legislation — such as proposals for shifting funds within Medicare or tax cuts to make it easier to buy insurance — but there is little consensus on those details.

Among the most contentious issues are how to structure Medicare and Medicaid and whether it is possible to promise that everyone who is insured under Obamacare will be able to find coverage under a GOP plan.

“My view is that replacement should try to get insurance for as many people as possible,” Paul said in an interview. “The administration likes to say that 20 million people are covered now. Well, 85 to 90 percent of that number got Medicaid. Many were already qualified for Medicaid. So a lot of debate goes into these numbers.”

Paul’s claim hugely overstates the extent to which Medicaid enrollees account for the insurance expansion.

Others, such as Cassidy, have pitched fully fledged replacement plans that have also failed to secure broad support. Cassidy said Monday that he wants to move quickly to repeal “onerous” parts of the health-care law, such as the requirement for individual health coverage, as long as there is a plan and timeline for completing a replacement.

“As long as we have a sense of where we’re going, I’m okay with that,” Cassidy said.

Cassidy’s proposal for that path forward includes costly provisions that would allow individual states to retain exchanges and would include a tax credit to help people buy insurance on the private market. The only problem: Nobody seems to know how to pay for those goodies.

David Weigel contributed to this report.