A top conservative group on Tuesday backed a potential framework for a new health care bill being floated by Vice President Pence, as the White House began courting Republicans to take another shot at overhauling ObamaCare – less than two weeks after they were forced to retreat on their first effort.

Club for Growth President David McIntosh told Fox News’ Bill Hemmer that despite them working with the House Freedom Caucus to kill the original bill, they could support the White House’s latest proposal. The initial endorsement could boost the chances of swaying conservatives concerned the initial bill did not go far enough in replacing the 2010 law.

McIntosh pointed to a new proposed provision that would allow states to apply for a federal waiver to opt out of what they see as cumbersome ObamaCare regulations.

“[We have to] see the language, see the bill, but if it’s there, I agree with Mike Pence that it’s a good provision and the bill should go forward,” he said.

Pence, who has been pushing the effort to House Republicans, met with House Speaker Paul Ryan Tuesday afternoon.

"The president and I remain confident that working with the Congress we will repeal and replace Obamacare with health care reform that will work for the American people and work for the American economy," Pence said.

Ryan said that while he believes the party is moving toward a consensus on the issue, he warned that they were still “at the concept stage now.”

Pence and Ryan’s meeting came after Pence met behind closed-doors with Freedom Caucus members as part of the bid to overcome the opposition that killed the first bill. Also present were budget director Mick Mulvaney and White House Chief of Staff Reince Priebus.

Freedom Caucus Chair Mark Meadows, R-N.C., called it a “good meeting” but members said they want to see the offer in writing before getting on board.

While courting conservatives, parts of the bill also look to allay the fears of moderates, such as the Tuesday Morning group. While the new proposal includes the ability for states to apply for a waiver from an obligation for insurers to cover “essential health benefits” such as mental health and maternity services, the failed bill removed that requirement completely -- only later allowing states to reimpose it on their own.

"The biggest change was putting the essential health benefits back in," said Rep. Chris Collins, R-N.Y. "That really took some Tuesday Morning group folks to yes from no."

It's unclear whether the new push could gain any more support on the Hill. A source in congressional leadership told Fox News the new health care plan may cost more votes than it brings in.

The issue shows the balancing act the White House must perform, as Freedom Caucus member Rep. Mo Brooks, R-Ala., said he remained opposed to the bill as he said states should be allowed to opt out of ObamaCare requirements without having to ask the federal government’s permission first.

McIntosh believes that conservatives now have what they want from the bill, and said the ball is now in the court of the moderates.

“Will Speaker Ryan and the moderates take a yes at this point?” he asked.

The Associated Press contributed to this report.