Will Trump’s nominee for deputy attorney general pledge to appoint an independent special prosecutor to investigate “the Trump campaign’s ties to Russia”?

That’s the question Democrats will be asking Rod Rosenstein during his confirmation hearing on Tuesday morning. Chuck Schumer, the Democratic Senate minority leader, said on Monday that this was “far and away the most important question” that Rosenstein would need to answer.

Richard Blumenthal, one of the Democrats on the Senate judiciary committee, pledged again on Monday to use “every tool, every power available” to slow Rosenstein’s confirmation if he would not promise to appoint a special prosecutor.

Schumer said a special prosecutor would have “greater latitude” to investigate Russia’s interference in the election, as well as “greater independence” to conduct the inquiry, since he or she could only be removed from the investigation for “good cause” and would have the power “to prosecute not only the subject of an investigation but anyone who attempts to interfere”.

The Republican chair of the Senate judiciary committee resisted these demands. “Nobody should be prejudging as to if there should or shouldn’t be a special prosecutor,” Beth Levine, a spokeswoman for Senator Chuck Grassley, said in a statement. “Mr Rosenstein should go into the job without any predeterminations and evaluate the necessity on the facts and the merits.”

The FBI is reportedly investigating Russia’s interference in the 2016 election, including scrutiny of links between Trump associates and Russia.

Under bipartisan pressure from Congress, the attorney general, Jeff Sessions, recused himself last week from overseeing any election-related investigations. Sessions failed to mention his election-year meetings with the Russian ambassador during his own confirmation hearing, despite a direct question about whether he had been “in contact with anyone connected to any part of the Russian government about the 2016 election”. Sessions later said he “should have” mentioned the meetings, but has also defended his response as appropriate given that he did not recall any conversations “regarding the political campaign on these occasions”.

Sessions’ recusal puts the deputy attorney general, the justice department’s second-highest ranking official, in charge of overseeing any investigations of Russian interference in the election.

Rosenstein, currently the US attorney in Maryland, is a widely respected career prosecutor with 26 years’ experience within the justice department. Former justice officials from Democratic administrations praised his skill and integrity, with one calling him a surprisingly non-partisan choice for a Trump administration appointee, and saying he was the “perfect” person to oversee a fraught political investigation that might touch on the White House itself.

Schumer and Blumenthal said they believed a special prosecutor should investigate not only Russia’s interference and any contacts between Moscow and Trump associates, but also whether members of the administration, including Sessions himself, had made “cover-up attempts” or tried to “meddle” in the investigation.

In a press conference on Monday, Blumenthal invoked the Watergate investigation of President Richard Nixon, when senators used the confirmation process to force the president’s attorney general nominee to promise to appoint a special prosecutor and guarantee him independence to carry out his investigation.

That same precedent should be followed in Rosenstein’s confirmation process, Blumenthal said.

Other Democrats on the Senate judiciary committee did not respond to requests for comment on Monday on whether they agreed with Blumenthal.

Democrats have acknowledged Rosenstein’s reputation as a “straight shooter” and “honorable” public servant, with Schumer calling him “a fair man”.

A CNN survey of about 1,000 American adults found that nearly two-thirds supported having a special prosecutor investigate links between Russia and Trump associates, including 43% of Republicans.

As a young Republican lawyer, Rosenstein was tapped to join Kenneth Starr’s independent Whitewater investigation into Bill and Hillary Clinton’s real estate dealings – an investigation that later pivoted to digging into Bill Clinton’s affair with a White House intern.