(CNN) Junior lawmakers on the House Judiciary Committee could get shut out of next week's highly anticipated hearing with special counsel Robert Mueller — and they're not happy about it.

The agreement reached between congressional Democrats and Mueller allowed for a limited time agreement where 22 members of the House Judiciary and Intelligence Committees would question the former special counsel. That's the exact number of members on the Intelligence panel, but includes just over half of the 41-member Judiciary Committee.

The arrangement has prompted an outcry, with junior committee Democrats publicly and privately grumbling about the arrangement and pushing for the committee to reopen negotiations so Mueller could potentially appear for a longer period. Republicans, meanwhile made their complaints loudly known at a Thursday hearing to vote on subpoenas , repeatedly criticizing House Judiciary Chairman Jerry Nadler for agreeing to limit the length of the hearing in order to get Mueller to testify.

Giving some members the chance to shine — while others will have to sit quietly at the panel's most-anticipated hearing in years — has created a headache for Nadler, because his members feel they're being robbed of the chance to press the special counsel in front of millions of people watching the proceedings,

"It's definitely a problem for only a couple of us to be able to ask questions," said Rep. Karen Bass, a California Democrat who would be in line to ask questions of Mueller.

"First of all, no hearing happens that way," she added. "I mean, the hearing goes until everybody's had an opportunity to ask a question. That's standard practice, that's what everybody's used to. But considering the significance of this issue, the fact that people have read the report, they want to drill down. That would be very, very frustrating,"

Others echoed those concerns.

"Absolutely," said California Rep. Ted Lieu when asked if he would be concerned if he's not allowed to ask questions.

Several committee Democrats -- who indicated they are mainly frustrated at Mueller for his unwillingness to testify longer -- have aired their concerns directly with Nadler, who has told them he would seek to accommodate them in his negotiations with the special counsel's team over the format of the hearing.

Ultimately, congressional sources said, Democratic leaders had to make a decision given that talks were dragging for months with Mueller, who didn't want to testify. Democrats had a choice: Should they push for unlimited testimony with the risk that Mueller would continue to refuse to appear and potentially defy a subpoena? Or should they cut a deal to get him sooner and ensure he appears, hoping they would be able to get what they needed in a shortened hearing. They chose the latter.

Still, it's a bitter pill to swallow for many lawmakers if the format doesn't change.

"I'll be disappointed, but I'm hopeful," said Pennsylvania Rep. Madeleine Dean, a freshman Democrat on the Judiciary Committee. "I feel it's part of my duty to be part of this oversight. Hopefully if I don't get public questions I get private questions. But I feel an absolute duty to fulfill this role."

Rank-and-file committee Democrats were able to raise their concerns at a closed-door member meeting Wednesday evening with members. It was a subject of debate inside the room, but Nadler suggested the senior members of the committee were the ones likely to do the questioning. However, he indicated they were still trying to work out some way for other members to get in on the action, according to multiple sources.

Several Democratic members who are not expected to get questions privately raised objections to the format, saying they argued all members should be able to ask questions given that they are all elected and they all have different constituencies to represent.

"I reminded the committee that — roughly two hours, a month ago we had zero hours. Let's take the time, let's use it wisely," said Rep. Val Demings of Florida, one of three members on both Judiciary and Intelligence. "I think if every member wants to ask a question they should be allotted that time. But we just have to be very strategic, very precise."

One option that's being proposed for the members who may be shut out is that they would ask questions during the closed-door session that's slated to follow the public hearing with Mueller. But the special counsel isn't expected to attend that session: two of Mueller's deputies would be answering questions if they ultimately appear.

"It is my expectation that in some form or fashion, everybody will participate in the hearing," said Rep. Hakeem Jeffries, a member of the House Judiciary Committee. "Either in open session or closed session."

The agreement for Mueller to testify for a limited period of time before the two committees was struck last month when the former special counsel agreed to appear if he was issued a subpoena. The agreement was made that he would appear before both the Judiciary and Intelligence Committees for an equal amount of time, as well as that both panels would get a chance to question Mueller's deputies.

But lawmakers from both parties have argued that the agreement flouts the House rules, which state that congressional hearings allow every member of a committee five minutes to question witnesses.

"You have the five minute rule of the House — that means every member," Lieu said. "You can't just ignore that rule."

At a separate committee meeting Thursday to vote on authorizing a dozen subpoenas related to the committee's obstruction of justice investigation, Republicans teed off on Nadler and the agreement that was struck.

"Next week, a hearing under one of the largest, most-talked about investigations in two years, and this committee got rolled," said Georgia Rep. Doug Collins, the top Republican on the panel. "Intel Committee gets to ask all their questions — this committee does not."

Collins told reporters after the vote that he has heard from Democrats who are unhappy.

"I'm hearing Democrats who are upset about it. They don't like it," Collins said. "They've come to me and said this is not right, not fair."

Other Republicans complained that they would not get to ask questions, and asked Nadler to explain his agreement with Mueller or consider alternative formats for the hearing. Nadler tried to avoid engaging with the Republican lawmakers, but did say he would "entertain any reasonable discussions."

"The question of the procedure at a hearing that we're going to hold is an important question, but it is not the subject of this markup," Nadler said. "Although I permitted people to talk about it and they can continue, I'm not going to add to the diversion of attention from the two crucial subjects we have here."

The House Intelligence Committee, which has had many of its own partisan brawls over the subjects of the Mueller report, is preparing for next week's hearing in a quieter manner.

On Thursday, the committee questioned David Archey, a senior FBI official on Mueller's team, behind closed doors, three sources familiar with the matter told CNN.

The meeting was separate from next week's hearing, the sources said. Intelligence Committee Chairman Adam Schiff of California has been demanding the FBI provide his committee with a briefing on the FBI's counterintelligence investigations related to Trump and Russia. Last month, he threatened to subpoena FBI Director Chris Wray if the FBI did not tell his committee whether any counterintelligence investigations are still active.

The Senate Intelligence Committee is also expected to receive a briefing from Archey, according to a source familiar with the matter.

A spokesman for Schiff declined to comment.