(CNN) House Republicans were on the verge of an immigration breakthrough Thursday, moderate lawmakers and sources said Thursday -- but only after the details are finalized and put on paper can the parties actually see if they agree.

For now, that progress seemed to buy GOP leaders more time before an immigration civil war erupts -- at least until next week.

The leaders of the effort that has been triggering weeks of intense negotiations -- a procedural maneuver that would force immigration to the floor and bypass party leadership -- said that conservatives had put forward a proposal to them that would include a "bridge" for recipients of the Deferred Action for Childhood Arrivals program and those like them to eventually gain citizenship, which has been the most difficult part of negotiations to date.

The proposal would create a new visa, moderate California Rep. Jeff Denham confirmed to reporters, and would offset the numbers of new legal residents by "combining" other visa categories -- likely eliminating some and reallocating the visas to cover the new category. There would be an eight-year process toward eventually getting a green card, Denham said.

But, he added, the devil is in the details.

"I don't think you can have any agreement until you see it in writing," Denham said.

But he said the key negotiators Wednesday night had a "productive conversation" that extended into a full GOP conference meeting that lasted two hours Thursday morning.

"Now it's a matter of putting it on paper and seeing if we actually have an agreement," Denham said. "But those of us in the meeting accepted what they were offering."

Still, others were quick to pour water on the emerging plan on the issue of citizenship for DACA-covered immigrants -- young undocumented immigrants who came to the US as children.

"No deal," said Freedom Caucus Chairman Mark Meadows.

"No. I don't see a deal yet," said Majority Leader Kevin McCarthy. "I see a lot of people talking, getting around the area they want to focus on, the four corners and stuff, but no one has said there is a deal yet."

As the details are hashed out, moderates have hit pause on signatures for what is known as a discharge petition , the moderates' attempt to bypass GOP leaders and force a set of immigration votes on the House floor. The procedural maneuver is just three signatures short of succeeding, including two Republicans.

Denham's partner in the effort, Florida Rep. Carlos Curbelo, said he expects House leadership to draft text of the emerging compromise in the next few days.

"The next two or three days will be decisive in terms of whether or not people keep their word and support this framework that is fairly detailed," Curbelo said. "There's still some blanks to be filled but it's fairly detailed right now. If people keep their word and support it, I think there's a potential that we don't proceed with the discharge petition."

But, he added: "If there's no agreement, then we're going to proceed."

A GOP leadership aide says that talks continue and there remains no actual "deal" or "plan" even if some agreements on pieces are being reached in theory. The aide also confirmed leadership is "coordinating" the process of getting agreements into legislative text.

Encouraged members

The reason moderates are optimistic about progressing negotiations, two sources close to the process said, is that the idea for the special visa came from conservative Freedom Caucus member Rep. Raul Labrador.

Meadows, however, said if Labrador is making offers, they are not on behalf of the Freedom Caucus.

Asked about reports that he offered the visa suggestion, Labrador said he would not get into the negotiations.

"I do not believe in a special pathway to citizenship, I have never talked about a special pathway to citizenship and I would never agree to a special pathway to citizenship," Labrador said.

But, the sources also cautioned, the specifics regarding who would qualify for the visa and what the thresholds would be remain key details to be worked out before a deal is reached. And the broader conference would have to accept the proposal once it is hammered out.

Multiple meetings

The progress came after House GOP members spent two hours behind closed doors huddling Thursday morning, a rare full-party confab on the issue of immigration.

Inside the meeting, according to multiple members leaving, House Speaker Paul Ryan and leadership started off by presenting some general options and ideas to the full conference, but then opened the floor to input. Ryan largely stuck to the President's areas of concern that he has articulated previously, and described different ideas to get there that have come from weeks of negotiation. And, as he tends to do, he used PowerPoint, members confirmed.

No one described reaching a consensus or plan, but still described the meeting as a productive exchange of ideas.

"If I knew what would get 218 Republican votes today, it would be on the floor," said Meadows, referring to the majority threshold in the House. "Obviously, there's not something today that would get 218 votes on the floor."

Meadows continued: "The pathway to citizenship remains still the thorniest issue that we have to deal with."

Also in the meeting was White House legislative aide Marc Short, who did not speak, according to Rep. Mark Walker, R-North Carolina. Members, including Walker and Denham, have said they have been in touch with White House aides including Short and top adviser Stephen Miller.

Still, moderates who support the discharge petition are hopeful the issue will be resolved.

"We're only three signatures away, but it's like the last two minutes of a football game," said Florida Republican Rep. Ileana Ros-Lehtinen. "It just goes on forever."