Chief Deputy Whip Rep. Patrick McHenry told reporters the White House gave the key representatives a "final offer" ahead of the planned vote. The White House has attempted to sweeten the deal for the conservative group.
"It's really in the hands of the members to accept or reject the White House's offer," the North Carolina Republican said.
House Speaker Paul Ryan's weekly news conference — which was set for 3:30 p.m. ET — was delayed until further notice.
Another Freedom Caucus member, Rep. Justin Amash, said Thursday that nothing new came out of the meeting with Trump, according to Reuters. The vote will fail if held Thursday night, he added.
White House press secretary Sean Spicer said Thursday he still expects the vote to take place later in the day. He added that "we have been very responsive" to concerns expressed by lawmakers.
"It's going to pass. So that's it," Spicer told reporters when asked what would happen if the bill did not pass.
Trump and Republican leaders have made health care their top legislative priority since Trump took office with a GOP congressional majority in January. While they ran on repealing Obamacare, Republicans walk a political tightrope, as most independent estimates have shown the current GOP plan will lead to more people uninsured.
Trump has said the repeal and replacement of Obamacare must happen before action can be taken on his other plans, including a major tax reduction. Republicans need 215 votes for passage.
Some public opinion polls have also shown that voters strongly oppose the proposal in its current form.
— NBC News contributed to this report
This story is developing. Please check back for further updates.