(CNN) Despite mounting pressure from the House Freedom Caucus to quickly repeal Obamacare, House Republican leaders insisted Tuesday morning that they would take a "step-by-step" approach to overhauling the Affordable Care Act.
The Freedom Caucus, a group of influential conservatives, publicly expressed their impatience Tuesday with Republican leaders for failing to schedule a vote to repeal the sweeping health care law. But GOP leaders are concerned about the political backlash that could come from swift and wholesale repeal of the health care law without having a replacement plan ready.
"Health care is very important to all Americans. We want to get it right and we've been taking our time to do that," GOP Rep. Greg Walden, the chairman of the House Energy and Commerce Committee, told reporters. "You're going to see us come forward with a replacement bill after we repeal that makes sure that people have access to affordable care health for the first time."
House Speaker Paul Ryan reiterated that the party is committed to both repealing and replacing Obamacare and said that leaders are taking a "step-by-step" approach.
Two senior GOP aides clarified to CNN afterwards that despite Walden's reference to "a replacement bill" that would come after Obamacare is repealed, there is no plan to consider one comprehensive legislation to replace what gets rolled back. Top Republicans are still considering a piecemeal strategy in which repeal and replace measures would be considered more or less at the same time, the aides added.
The remarks came just hours after members of the Freedom Caucus backed a proposal to immediately bring up a repeal bill that Republicans passed in 2015 to roll back Obamacare. Leaders from the Freedom Caucus will also roll out their own Obamacare legislation on Wednesday, and members of the group stress it will include provisions to both repeal and replace the law at the same time.
"We made a commitment to the American people to repeal this law -- we must keep that promise," the caucus said in a statement Tuesday morning. "We remain open to and encourage a swift vote on a health care package that is market-based, consumer driven, and fair."
Idaho GOP Rep. Raul Labrador urged fellow Republicans to follow through on pledge to dismantle Obamacare.
"Members of Congress are scared all the time," he said. "They need to just lean in."
House conservatives in the House say they are getting nervous that some senators are softening on Obamacare repeal and that some Senate Republicans from state that have expanded Medicaid are especially weary of moving the process along quickly.
GOP Rep. Dave Brat, a member of the Freedom Caucus, referred to the 2015 repeal legislation as "the only politically expedient piece to push."
"If you add anything to it, the Senate probably flies away," Brat said.
"Let's just call it a hunch," said GOP Rep. Trent Franks added.
One GOP source familiar with the vote told CNN: "There's no reason we shouldn't be able to pass this ASAP -- there's also no reason we should send anything less to President Trump's desk than we did Obama's. No need to reinvent the wheel."
But since President Donald Trump's inauguration, many congressional Republicans have asked party leaders to slow down the repeal efforts to ensure that a consensus is reached on an Obamacare alternative. Top Republicans are still weeks away from completing a repeal legislation, which now aims to include various replacement measures.
Republicans have previously used the budget reconciliation process to repeal major portions of Obamacare (in 2015, it was vetoed by President Barack Obama).
Conservative House Republicans have become more vocal in recent days in pressing GOP leaders to move that same 2015 repeal bill rather than taking more time to craft a new version.
"For goodness sake, we should be able to put something on President Trump's desk that's at least as good as what we put on President Obama's desk. Not something watered down," Rep. Jim Jordan, R-Ohio, told CNN in a recent interview. "Let's repeal it. Let's do what the voters sent us here to do."
In a meeting Tuesday morning, House leaders announced to colleagues that there will be an all-conference policy planning meeting on Thursday to continue the repeal and replace discussions, according to source in the room. At the Tuesday gathering, Walden, along with Rep. Kevin Brady, the chairman of the House Ways and Means Committee, presented on replacement plans, and plan to get into more of the details on Thursday, that source added.