(CNN) Patience is wearing thin over Robert Mueller's testimony as Democratic members are ratcheting up their calls to subpoena the special counsel.

Rank-and-file members on the House Judiciary Committee are increasingly saying that it's time to compel Mueller to testify publicly before their committee, even if he prefers not to appear in such a setting.

"It is my hope that that's going to happen in very short order," said Rep. David Cicilline, a Rhode Island Democrat, when asked if the committee should subpoena Mueller. "I think there is still some hope that there will be an agreement reached that the special counsel will come voluntarily, but I think the chairman has made it very clear that he intends to be certain that the American people hear from Mr. Mueller, and if that requires a subpoena, I have every confidence the chairman will issue one."

Mueller's possible testimony has loomed over the committee for weeks following his public statement last month , which emphasized both that the special counsel investigation did not exonerate President Donald Trump — and that Mueller did not wish to testify publicly before Congress.

Since then, Judiciary Chairman Jerry Nadler has said he's confident Mueller would testify, and the New York Democrat would subpoena Mueller if necessary, which he told Democratic leaders earlier this month could happen "within weeks." House Intelligence Chairman Adam Schiff has also threatened a subpoena to Mueller for his testimony, saying the California Democrat's committee should speak to the special counsel behind closed doors about the counterintelligence portion of the investigation.

Democrats have been calling for Mueller's testimony since he wrapped up his investigation earlier this year, while they grapple with whether to begin an impeachment inquiry into Trump following up on allegations outlined in the report. They've argued that Mueller's 448-page document did not break through with the American public, but a high-profile televised hearing could do so.

"It's important for the American people to see and to hear what the report found, and to hear questions about it," Nadler said in a WNYC interview last month.

Nadler has declined to comment to reporters this month on the status of negotiations with Mueller for his testimony or the timing of a potential subpoena. Democrats say they think Mueller needs to appear before the end of next month, after which Congress will leave Washington for a month-long August recess.

"We're going to need to hear from Bob Mueller sooner rather than later," said Rep. Hakeem Jeffries, the Democratic caucus chairman and a Judiciary Committee member. "In my view, we need to hear from him before Congress recesses in August for the district work period."

But the impasse has even prompted Republicans on the committee to begin needling Nadler about Mueller's testimony. Georgia Rep. Doug Collins, the top Republican on the committee, has suggested that Democrats haven't subpoenaed Mueller because they don't actually want to hear from him, since the report did not establish a criminal conspiracy with Russia.

Rep. Matt Gaetz, a Florida Republican, went directly to Nadler at Thursday's hearing on the Mueller report where expert witnesses testified. "Mr. Chairman are you going to subpoena Robert Mueller? I'll yield to you to answer," Gaetz asked.

"I'm not going to answer that at this time," Nadler replied.

Democrats say Mueller's testimony is even more important because the White House is blocking witnesses from testifying — or even appearing — to discuss episodes from the White House outlined in the Mueller report.

As Democrats wait for Mueller, the Judiciary Committee has instead held public hearings with subject matter experts, like Thursday's hearing, in an effort to illustrate the report's findings. But they acknowledge that expert testimony is no substitute for the special counsel.

"I know that they're in negotiation, but you know, time has passed and so, if he's not going to issue it today, if Mr. Mueller doesn't cooperate, I'm sure it will be issued soon," said California Rep. Karen Bass, a Democrat on the Judiciary Committee.

Mueller gave his first and only public statement about his investigation last month, in which he said that the special counsel's investigation could not come to a conclusion on obstruction of justice because of a Justice Department opinion on indicting a sitting president. Mueller's comments prompted a wave of Democrats to call for beginning an impeachment inquiry into the President.

But in the same statement, Mueller also said that he didn't want to testify because any congressional testimony would not go beyond the findings of his report.

"The report is my testimony," Mueller said.

That answer, however, has not satisfied Democrats, who say they have additional questions for Mueller, including why his office didn't pursue certain investigative tracks.

Asked Thursday whether it was time to subpoena Mueller, Rep. Ted Lieu said: "I do."

"One of the expert witnesses on election law today testified that he believe special counsel Mueller did not go far enough in exploring violations of our federal election laws," the California Democrat said. "I would like to ask special counsel Mueller why their team didn't do that."