Washington (CNN) The rag-tag rabble-rousing House Freedom Caucus may be the linchpin to repeal and replace Obamacare at this point.

Its members, however, are Public Enemy No. 1 on Capitol Hill.

The group of conservative agitators who've irked leadership, held the line against spending bills and rebelled against trade priorities of leaders have now helped delay a health care vote at least one day.

Lawmakers and staffers are taking out their unhappiness on the group.

Even the White House is getting frustrated, sources say, as meetings -- -- including one Thursday morning with President Donald Trump -- have gotten them nowhere.

Rep. Bradley Byrne, an Alabama Republican and member of the Republican Study Committee, a large group of fiscal conservatives, complained Thursday morning that the Freedom Caucus continues to throw out an expanding list of demands and suggested there was little to be done to get some in that group on board and it was time to move on.

"Those members don't change so at some point you've got to say there's nothing in the world that's going to change their minds," Byrne said.

A senior GOP aide said the caucus realizes they have moderates at risk with nothing to show for it.

"They don't know how to get to yes. They just don't. And it's putting the whole process at risk right now," the aide said.

Byrne blasted the move to continue talks with the hard right in the Freedom Caucus while leaving the bulk of other members in the dark.

"The vast majority of us in the Republican conference have been left out of these discussions and we have no idea what's going on, and I think that is a problem for our leadership and I think it's growing problem for the chances of this bill," Byrne, who is supporter of the health care bill and part of the whip operation to help pass it.

Freedom Caucus Chairman Mark Meadows, R-North Carolina, said Thursday there are "30-40" votes against the bill at this point. He also tried to downplay his power.

"I don't have any veto power," Meadows told reporters. "I have one vote."

So what is the Freedom Caucus, anyway?

A brief history

The House Freedom Caucus got its start in 2015 when a small group of members came together to push for more conservative spending and policy ideals in the House. At first, there were just nine of them, but the group, which is considered the most far-right flank of the Republican conference, grew.

Who is in it?

There is no official list of members, but the group is currently led by Rep. Mark Meadows, a North Carolina Republican. Other prominent members include Ohio Rep. Jim Jordan, Idaho Rep. Raul Labrador, Alabama Rep. Mo Brooks, South Carolina Rep. Mark Sanford and Michigan Rep. Justin Amash.

What have they accomplished?

The group -- when they hold the line together -- can have a lot of influence.

In 2015, they pushed to defund Planned Parenthood in a must-pass bill to keep the government funded. The group's revolt against then-House Speaker John Boehner on a host of issues left Boehner ready to retire. During the Obama years, many of the conservative bills that made it through the House never had a shot of being signed by former President Barack Obama. Now, the group could have a lot more sway.

And while the group has insisted its relationship with House Speaker Paul Ryan is more open, the opposition by much of the group to House leaders' health care bill has created a schism once again between the group and leadership.

Why they matter now

The group has said repeatedly that it has the votes to kill House leadership's health care bill, and members seem to have enough sway with the White House that they've continued negotiating with Trump even after House leaders indicated no more changes would likely be made.

The Freedom Caucus may get a repeal of Essential Health Benefits to be included in the House leadership's bill. That would repeal the requirement in Obamacare that insurers cover 10 benefits such as maternity care and prescription drug coverage. Including it in the bill could substantially frustrate moderates who want to be a 'yes' but worry that their constituents would be irate if they take away the benefits.