House Democrats on Thursday unveiled a proposed resolution that would grant congressional committee chairs sweeping new powers to unilaterally "initiate" judicial proceedings to enforce subpoenas in federal court, as long as they first obtain the sign-off of a small, Democrat-dominated group of House leaders.

The resolution, obtained by Fox News and set for a vote before the full House on Tuesday, marks a dramatic escalation in Democrats' ongoing efforts to continue to keep multiple investigations of President Trump and his administration alive -- even as the White House has vowed not to comply with what it calls an attempted "do-over" of Special Counsel Robert Muller's Russia probe.

Ordinarily, Democrat-led committees would need to secure a vote of the full House before seeking to enforce subpoenas in court. By allowing committee chairs to act without a full House vote in the future, leaders could avoid tying up precious floor time — and also prevent Democrats from more conservative districts from taking multiple votes on contempt resolutions. Many of those members have said they would prefer to be working on policy instead of investigations of the president.

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Committee chairs, under the resolution, could take the administration to court with the approval of a majority of handful of senior leaders in the House, dubbed the "Bipartisan Legal Advisory Group." The list includes Democrats Nancy Pelosi, Majority Leader Steny Hoyer, and Majority Whip Jim Clyburn, as well as GOP Minority Leader Kevin McCarthy and Minority Whip Steve Scalise.

“We will not allow this president and his administration to turn a blind eye to the rule of law," Rules Committee Chairman James McGovern, D-Mass., said in a statement.

“There’s a concern that there could be a lot of floor time eaten up if we handle these one at a time," a Democratic congressional aide told Politico. “We are carefully prioritizing the fights we choose to elevate to this level.”

Separately, the planned resolution would also authorize contempt cases against Attorney General William Barr and former White House counsel Donald McGahn for allegedly failing to comply with subpoenas.

Barr has defied a subpoena to provide a full and unredacted version of special counsel Robert Mueller's Trump-Russia report, along with underlying evidence from the report. Republicans have asserted that federal law protecting secretive grand-jury information would prevent Barr from turning over all of those documents, and Mueller himself has said he does not question Bar''s "good faith" in his handling of the report's release.

McGahn, who is frequently referenced in the report, has also defied subpoenas to provide documents and testify before the Judiciary Committee. The White House directed McGahn not to comply with requests for documents during his tenure there, saying he is legally immune from being compelled to testify about privileged discussions in the course of his official duties. Democrats have responded that McGahn waived that privilege by agreeing to speak to Mueller.

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Former communications director Hope Hicks and a former aide to McGahn, Annie Donaldson, also defied subpoenas this week at the request of the White House. The administration said they don't have the legal right to turn over documents from their time working for Trump.

At the opposite end of the Democratic caucus, several of the most liberal members are pressuring House Speaker Nancy Pelosi to open impeachment proceedings against Trump. But Pelosi has so far rejected that option, preferring a slower, more methodical approach to investigating the president — including the court fights.

As part of the step-by-step effort endorsed by Pelosi, the Judiciary Committee will hold a series of hearings on "crimes and other misconduct" in Mueller's report, starting with a hearing on Monday, the day before the contempt votes, on whether Trump committed obstruction of justice. That hearing will feature John Dean, who was White House counsel for President Richard Nixon, and former U.S. attorney

Trump, for his part, has emphasized he did not assert executive privilege to shield any aspect of the Mueller report itself, and has derided Democrats' efforts as politically motivated attempts to keep what he's called the "Russia collusion hoax" alive -- and to distract from, or derail, Barr's own ongoing probes into Justice Department and FBI misconduct.

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News of the planned contempt vote came days after Barr said he has not received answers from the intelligence community that were "at all satisfactory" in the early stages of his review into the origins of the Russia investigation.

Last month, Barr appointed U.S. Attorney from Connecticut John Durham to lead the investigation, which is to focus on the use of FBI informants and the alleged improper issuance of Foreign Intelligence Surveillance Act (FISA) warrants to monitor a variety of individuals, including former Trump aide Carter Page.

The DOJ, meanwhile, continues to communicate with the House Judiciary Committee. The department earlier this week said it was "prepared to resume negotiations with the committee regarding accommodation of its narrowed Subpoena" -- as long as Democrats removed the "threat of an imminent vote by the House of Representatives to hold the attorney general in contempt."

The threat apparently remains, but House Judiciary Committee Chairman Jerry Nadler said late Tuesday that he is open to negotiating with the DOJ "without conditions."

Fox News' Chad Pergram, Alex Pappas, and The Associated Press contributed to this report.