Bob Casey, D-Pa., said he doesn't have high hopes for what will be made available either to the public or to Congress but is keeping his fingers crossed he is wrong.
Barr sent Congress a letter on March 24 summarizing Mueller's main conclusions.
In his letter, Barr said the special counsel did not find a criminal conspiracy between Russian Federation and Donald Trump's associates during the campaign, but Mueller did not reach a conclusion on whether Trump obstructed justice.
Democrats also are skeptical of Barr's conclusion because he has always been opposed to the special counsel investigation and was hired by Trump.
On "Outnumbered" Monday, Capri Cafaro said she expects some Democrats and Trump adversaries to claim that the redacted portions of the report are "hiding" potential evidence of Trump-Russia collusion or obstruction of justice.
Barr said he and Mueller were working on color-coding redactions to the report, broken into categories, including grand jury information, information that would reveal intelligence sources and/or methods, and information that could interfere with ongoing spinoff prosecutions, and Information that implicated the privacy of "peripheral players" not being charged with any crime.
Barr has pledged to be as transparent as possible.
Justice Department regulations give Barr, a Trump appointee and the top US law enforcement officer, broad authority to decide what to release and what to withhold from the report. Barr previously said the report is almost 400 pages long.
But the extent of Barr's redactions could prove controversial and leave many dissatified.
As Barr's standoff with House Democrats continues, at least one influential Republican - Representative Devin Nunes - has signed on to an effort to demand that the Attorney-General provide the House Intelligence Committee with any redacted intelligence and counterintelligence information Mueller considered in compiling his report.
He added, "I do think there should be a concern, though, in knowing what has happened with respect to the Hillary Clinton and Democratic National Committee-funded dossier, where they actually hired a retired former intelligence officer that was British for the purposes of talking to Russians and then use that information in a way where the government used it to undertake surveillance on the other campaign". Last week, Barr told a U.S. Senate panel he believed that "spying" did occur on Trump's campaign, and he plans to investigate whether it was properly authorized.
This means full analysis of the report will come out on Friday.
Mr Montoya said it should fall to Congress to decide whether conduct discovered by Mr Mueller's team warranted an effort to remove the president from office.