Tuesday is shaping up to be a rough day for Attorney General Jeff Sessions, who is expected to be grilled during an appearance before the House Judiciary Committee by both Republicans and Democrats. Both parties are unhappy with his job performance.

Two House Republicans expressed frustration Monday that the attorney general has not appointed a special counsel to investigate FBI Director James B. Comey’s handling of last year’s election, and suggested that he either appoint an independent investigator or resign and clear the way for someone who will.

House Democrats, meanwhile, put Mr. Sessions on notice last week that they intend to question him about “inconsistencies” in accounts the attorney general has given about his knowledge of Russian interaction with members of the Trump campaign, when the then-senator served as a top security-policy adviser.

Mr. Sessions appearance before the House committee comes two weeks after the first criminal charges against members of President Trump’s 2016 campaign were unsealed — offering new information about Russian efforts to arrange meetings with Mr. Trump or members of his campaign.

Democrats said the case revealed George Papadopoulos, who served as a foreign policy adviser to the Trump campaign, admitted to informing Mr. Trump and Mr. Sessions at a March 2016 national security meeting that he had connections who could help arrange a meeting with Russian President Vladimir Putin.

“In other words, officials at the highest level of the Trump campaign knew about Mr. Papadopoulos’s interactions with Russian officials on behalf of the campaign and hoped to hide these interactions from the public,” wrote House Democrats in a letter sent last week to Mr. Sessions. “These facts appear to contradict your sworn testimony on several occasions.”

Mr. Sessions has said he had no knowledge of communications between Trump figures and Russian operatives.

His own description of connections has evolved, from an initial denial of his own contact with any Russian officials during the course of the Trump campaign to later admitting he had meetings with the Russian ambassador.

“You answered no, you concealed your own contact with Russian officials at a time when such contacts were of great interest to the committee,” Sen. Patrick Leahy, Vermont Democrat, said during a Senate committee hearing last month of questions the committee asked Mr. Sessions to address during his confirmation hearing.

The attorney general defended his response, saying he believed it was correct given the context.

“I took that to mean, not any casual conversation, but ‘Did I participate with the Russians about the 2016 election?’” Mr. Sessions said. “Every one of your previous questions talked about improper involvement and I felt the answer was no.”

While Democrats’ criticism has focused on the ongoing Russia investigations, Republicans are worried that Mr. Sessions has not provided the American people enough information about actions the Justice Department took during the last administration as the campaign was ongoing.

Reps. Jim Jordan of Ohio and Matt Gaetz of Florida said questions are piling up over the way Mr. Comey conducted the investigation of former Secretary of State Hillary Clinton’s secret email server and the FBI’s treatment of an anti-Trump dossier.

“It’s time for Jeff Sessions to name a Special Counsel and get answers for the American people. If not, he should step down,” the congressmen said in an op-ed for FoxNews.com.

They said Mr. Comey’s decision to draft an exoneration letter regarding Mrs. Clinton months before the end of the investigation, and well before the FBI talked to her, was troubling.

They also expressed concern over Mr. Comey’s handling of the anti-Trump dossier. They said if it was so concerning, the director should have briefed the president-elect well before the Jan. 6 briefing Mr. Comey delivered.

And the congressmen said the 2010 deal that saw the U.S. approve sale of uranium to Russian interests demands a more thorough investigation, saying it calls into question the independence of special counsel Robert Mueller, who is probing Trump campaign figures’ work with Russia.

While Mr. Sessions’ appearance Tuesday is before the House, Mr. Leahy and Sen. Al Franken, Minnesota Democrat, took to the Senate floor Monday to demand that he also appear before the Senate Judiciary Committee again.

“It is clear that Attorney General Sessions has an ongoing difficulty remembering his own interactions with Russians. As the record demonstrates Attorney General Sessions has misrepresented the truth about those contacts to members of this body time and time again,” Mr. Franken said. “The inability of our nation’s top law enforcement official to speak with a clear and consistent voice about what he knows of the Russian operation is disturbing.”