(CNN) Republicans are focused on trying to come together after a major setback last week to repeal and replace the Affordable Care Act -- and they aren't entirely ready to move on.

Emerging from their first conference meeting since the setback, Republican members said the message from their leadership was direct: it's time to unify.

"I think it was the longest prayer we've ever had," New York Republican Rep. Chris Collins said, referring to the opening prayer that is part of every conference.

Many members emerging from the Tuesday morning meeting said the GOP wasn't yet ready to abandon health care despite the fact that President Donald Trump made it clear last week it was time to get on to tax reform.

To that point, the White House has quietly re-engaged on health care in recent days, despite the very public proclamation last week, according to two people familiar with the process.

The efforts, while unclear how effective or deep they may be, have been driven by chief strategist Steve Bannon and Health and Human Services Secretary Tom Price, who believe there is a way to bridge the gap that helped collapse the effort, the sources said.

The paralyzing issues for the conference remain unchanged, however. Significant shifts toward the conservative House Freedom Caucus would only serve to drive even more moderate members away from the bill. Move the bill back toward the center and the Freedom Caucus will buck the effort as a bloc. The bigger issue may be the President himself, who made clear his patience had run out on the issue and was champing at the bit to move onto tax reform.

North Carolina Rep. Richard Hudson said if Republicans could find the votes, the House could again bring up last week's bill as early as this week, noting that the House Freedom Caucus was "probably feeling a lot of heat."

Asked about the White House posture, Hudson told reporters, "I think if we called the President today and said, 'We've got the votes,' I think he'd be back on board."

During their leadership news conference Tuesday morning, Republican Whip Steve Scalise of Louisiana said that Democrats' celebration Friday had been "premature."

"To my Democrat colleagues who were celebrating Friday's action, I think their celebration is premature because I think we're closer today to repealing Obamacare than we've ever been before, and are surely even closer than we were Friday," Scalise said.

House Speaker Paul Ryan also said Republicans would continue to push for repeal and replace.

"I won't tell you the timeline because we want to get it right," Ryan said, adding that members had a "very constructive meeting" where some who had pledged to defeat the bill last week appeared open to working with the rest of the conference to find a solution.

Ryan specifically advocated that the health care bill was still the best path to defund Planned Parenthood, a key conservative agenda item. The Wisconsin Republican said the health care bill was a better option for defunding the organization than including the provision in the upcoming must-pass spending bill.

"We think reconciliation is the tool because that gets it in law," Ryan said. "Reconciliation is the way to go."

Rep. Mo Brooks, a Republican from Alabama and a member of the House Freedom Caucus, said the message from Ryan was "this issue is not going away."

Iowa Rep Steve King told reporters that the discussion at Tuesday morning's meeting reminded him of an impasse that House Republicans faced in 2014 on a border security bill. "we circled back together and we resolved the issue. I think that mood exists today." He added, "the minds that have been in the starkest disagreement are now going to put their heads together."

Members of the hard-right wing of the conference seemed committed to not move on from health care. House Freedom Caucus Chairman Rep. Mark Meadows told reporters that he and others still wanted to get to "yes."

Meadows told reporters after the extended closed door meeting, "everybody wants to find a way to get this passed and we're going to work real hard to do that."

"We're going to get a yes. We're going get to yes. It will be a better bill. And I think everyone is going to be very happy in the end," said Virginia Rep. David Brat, a member of the Freedom Caucus.

Meadows told reporters after the extended closed door meeting "everybody wants to find a way to get this passed and we're going to work real hard to do that."

Rep. Barry Loudermilk, a Republican from Georgia, said every House Republican who went to open mic during the GOP conference meeting pushed to get health care done.

"It's halftime," he said. "The game isn't over and it's not starting over again. We're just coming back out after halftime and we still have the ball and we're going on the field."