Washington (CNN) House Democrats advocating for impeachment say special counsel Robert Mueller's testimony next month could be a game-changer to push both public opinion and reticent Democrats toward opening an impeachment inquiry into President Donald Trump.

But Mueller's appearance amounts to a make-or-break moment for the House impeachment caucus. If the special counsel's testimony falls flat or doesn't change minds, it could deflate the momentum for impeachment that's swelled to nearly 80 House Democrats backing an inquiry just before a lengthy, month-long congressional recess.

Tuesday's announcement that Mueller would testify publicly on July 17 before the House Judiciary and Intelligence committees has been weeks in the making, as Democrats and some Republicans have pressed for the special counsel's appearance , even after he publicly said he did not want to testify. For Democrats backing an impeachment inquiry, Mueller's testimony is a prime opportunity to sway public opinion on the special counsel investigation that they feel was tainted by the way Attorney General William Barr presented his findings.

"It's the best evidence. If he just talks about the report, it'll make more people realize the criminal behavior that (Trump) engaged in," said Rep. Steve Cohen, a Tennessee Democrat who has sponsored an impeachment resolution.

"The pressure to impeach grows every single day, and I think that having testimony, public testimony, from Robert Mueller will add credence to the case, and that it only adds to the pressure once his statements are made public," said Rep. Alexandria Ocasio-Cortez, a New York Democrat who backs an impeachment inquiry.

House Speaker Nancy Pelosi has resisted the Democratic calls to begin an impeachment inquiry, arguing that it's a step that should only be taken with public backing and bipartisan support. Pelosi on Tuesday praised the applauded the news Mueller is set to testify, but it's not clear whether that will change her calculus on impeachment.

Democratic leaders are already being cautious not to overhype Mueller's appearance, given that Mueller did not want to testify and has stated he will not say anything beyond what was written in the report.

"I don't think people should have excessive expectations," said House Intelligence Chairman Adam Schiff. "It's going to be very important to bring him in and to be able to hear from him. Certainly the outlines of what he's going to talk about is in the report, now many Americans haven't read the report, again, I think we should be realistic about our expectations."

Rep. Jim Himes, a Connecticut Democrat on the Intelligence Committee who publicly called for an impeachment inquiry this week, said it was important for the public to hear from Mueller but predicted there likely weren't new revelations coming.

"My colleagues are going to spend a day trying to get him to say things outside of the report, and I think he's unlikely to do that," Himes told CNN's Kate Bolduan. "If you go into this believing what he has said, which is that his report is his testimony, I think the only risk is that there's going to be a feeling of letdown."

On Wednesday afternoon, Trump reiterated his longstanding claims that there was no obstruction in the investigation or collusion between his campaign and Russia.

"This is a disgraceful thing. I heard about it last night and I just said does it ever end? At what point does it end? It's a disgrace," Trump told reporters at the White House before departing for Japan.

'The TV version of the Mueller report'

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The Democrats pressing Pelosi to change course on impeachment predicted momentum would grow following Mueller's appearance. It's a high-stakes gambit that could have a short window of opportunity, however, because Mueller is coming to Capitol Hill just days before the month-long congressional recess begins in August, and the long summer break risks diluting the push for an impeachment inquiry.

Impeachment supporters argue that Mueller's testimony provides an opportunity to shift public opinion in their direction in a way that the release of the dense, 448-page special counsel report simply could not.

"I have always thought that we need to have the TV version of the Mueller report, he does not need to go beyond the report itself, it's all there," said Rep. Jan Schakowsky, an Illinois Democrat who supports opening an impeachment inquiry. "All the obstruction of justice is there, all of the interference with our election is in the volume one — they're all there."

House Judiciary Chairman Jerry Nadler and other Democrats have argued that Barr misrepresented Mueller's findings through a four-page summary that Democrats say glossed over the episodes of obstruction of justice Mueller documented and the numerous contacts between Russians and Trump's team.

Nadler said Wednesday he didn't know how Mueller's testimony would change the dynamics of the impeachment debate, but argued that it had the potential to have a "profound impact."

"I think that given the nature of what he has to say, given the nature of what was in the report, he will be a very compelling witness," Nadler said.

Republicans were skeptical.

Rep. Doug Collins, the top Republican on the Judiciary Committee, said he didn't expect Democrats to learn anything new from Mueller's testimony. "I think that's one of the reasons why they finally decided to move on this. This is not a victory. It's something they should have done a long time ago," Collins said.

Senate Judiciary Chairman Lindsey Graham, who has rebuffed calls from Democrats on his panel to bring in Mueller, said he didn't think Mueller's testimony would change minds -- and warned it could backfire for Democrats, too.

"It can blow up in their faces as much as anything else," Graham told CNN. "It's going to be a political circus. ... I think the public has pretty well made up its mind."

Mueller's public comments swayed some lawmakers

But to Democrats who support an impeachment inquiry, Mueller's words are essential.

When the special counsel last month spoke publicly for the first time since his May 2017 appointment, his comments sparked a wave of House Democrats to call for an impeachment inquiry. Their numbers quickly rose with some moderate Democrats joining the ranks of liberals who have pushed for impeachment since Democrats won back the House in November.

"Mueller's words are powerful, hearing them from him is powerful, and I think the American people need to hear them," said Florida Democratic Rep. Val Demings, who sits on both the Judiciary and Intelligence Committees.

"The members will get where they need to be, but it's really about helping the American people understand really what the impeachment process is all about," Demings added.

California Rep. Karen Bass, who leads the Congressional Black Caucus and has not backed an impeachment inquiry, said Wednesday it was possible Mueller's testimony could persuade her. But she wanted to see how the public reacted.

"I think it's going to be really important to gauge how the public will respond," Bass said. "Because I think since Barr tainted the report, intentionally in my opinion, to discourage people to read it -- why bother because Barr said there's nothing in the report -- that when people hear Mueller's words, we'll see if that makes a difference."

To some Democrats weighing impeachment, seeing Mueller's evidence is more important than hearing from him directly, and both the Judiciary and Intelligence Committees have battled the Justice Department to obtain the materials that shaped Mueller's findings.

"He's not a fact witness, but I do think he will shed light on the entire report, as well as his staff," said California Rep. Zoe Lofgren, a senior Democrat on the Judiciary Committee. "The fact remains we have to examine direct evidence."

Michigan Rep. Justin Amash, the lone congressional Republican who has backed impeachment, said he wanted Mueller to go beyond what was in written in his report. "I want to hear him tell the story to the American people," he said.

Asked whether Mueller's testimony could influence the impeachment debate, Amash demurred: "It will really depend on what he says."