The White House has sought to revive talks with congressional Republicans on the American Health Care Act, the bill aimed at overturning Obamacare -- also known as the Affordable Care Act.
House Speaker Paul Ryan stated on April 4 that talks were in the preliminary stages, according to The Hill.
"Right now, we’re just at that conceptual stage about how to move forward in a way we can get everybody to 216 [votes]" said Ryan, according to The Hill.
"It's important that we don't just win the votes of one caucus or one group," Ryan added, The Washington Post reports.
Republicans require 216 votes in the House to ensure the passage of the legislation.
Speaking at an event at the White House, Vice President Mike Pence said he and President Donald Trump "remain confident" that Obamacare will be repealed.
The White House has reportedly suggested a new proposal that would see the federal authorities grant states a waiver from some Obamacare provisions. More details are expected to be released later on April 4.
The waivers could enable states to be exempt from "essential health benefits," which include requirements for insurance policies to cover mental health conditions, maternity care, substance abuse and prescription drugs.
Several Republicans indicated that they have not yet been convinced to shift their position.
"There have been no changes from no to yes because we haven't seen the text," Republican Rep. Mark Meadows of North Carolina and chairman of the right-wing Freedom Caucus said, according to Politico. "And so at this point there's ... only a willingness and an openness to look."
The Freedom Caucus vowed to vote against the bill on March 24, which was a major factor in Ryan's decision to pull the measure prior to the House vote.
In addition to right-wing critics, some moderate Republicans also have concerns about the legislation, which are likely to increase if concessions are made to the Freedom Caucus.
"I have seen nothing in terms of reported possible changes to American Health Care Act warranting reconsideration," Rep. Frank LoBiondo of New Jersey, a moderate Republican, tweeted. "I remain a NO."
Republican Rep. Charlie Dent of Pennsylvania, one of the chairmen of the moderate Tuesday Group, backed up LoBiondo.
"My position remains the same," Dent told Politico. "I'm still opposed to the bill in its current form, even with the changes I've heard suggested."
Anonymous officials speaking to Politico suggested the Trump administration is playing a more active role than it previously did, with one stating that the "White House is taking the lead this time."
Pence, Trump's Chief of Staff Reince Priebus and Budget Director Mick Mulvaney attended a meeting of the Freedom Caucus on April 3. Meadows told The Washington Post that they presented a "solid idea" aimed at achieving a compromise among Republicans.