Democrats considering whether to impeach Donald Trump “can sing and dance at the same time just like Beyoncé”, a member of party leadership said on Sunday as debate on the issue raged on.

After special counsel Robert Mueller laid out 11 instances of possible obstruction of justice and as the White House blocks oversight moves by the House, calls for impeachment have grown.

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But party leaders have pointed out that Trump’s removal would require a two-thirds majority in the Republican-held Senate, a vastly unlikely outcome in a body firmly in thrall to the president. Democrats also fear boosting Trump at the polls.

On Sunday the New York congressman Hakeem Jeffries, chair of the House Democratic caucus, made the Beyoncé analogy when he told NBC’s Meet the Press the party could check Trump and serve its voters at the same time.

Democrats should “focus primarily on our For the People agenda”, he said, adding: “We don’t work for Donald Trump. We work for the American people.

“We have a constitutional responsibility to serve as a check and balance on a potentially out of control executive branch. But we will not overreach. We will not over-investigate, we will not over-politicise that responsibility.

We will proceed as Speaker Pelosi has eloquently laid out, methodically yet aggressively to get to the truth Hakeem Jeffries

“We will proceed as Speaker Pelosi has eloquently laid out, methodically yet aggressively to get to the truth.”

From the progressive wing of the party, the Michigan representative Rashida Tlaib – who last November famously told supporters it was time “to impeach the motherfucker” – said oversight was not working and impeachment was “about doing what’s right now for our country”.

“For me,” she told NBC, “to fight back against Big Pharma, for many of my colleagues that came [to Congress] to pass really important reforms that are needed, we can’t do it when the president of the United States continues to lie to the American people, continues to not follow through on subpoenas and give us the information that we need.”

White House officials and senior Republicans defended a move by Trump that has added fuel to Democratic fires: the decision to give the attorney general, William Barr, authority to declassify material related to the origins of the Russia investigation, and to order the US intelligence community to co-operate.

Special counsel Robert Mueller did not find evidence of a conspiracy between Trump and Moscow over Russian election interference. But in the redacted version of his report that has been made public he did lay out extensive evidence of contacts between Trump aides and Russians and explicitly did not clear the president of obstruction of justice.

Nonetheless, and over howls of protest from Congress, Barr said he would not pursue the matter and Trump has claimed exoneration.

Trump seems convinced he is the victim of a vast leftwing conspiracy. Earlier this month, for example, he tweeted that his campaign was “conclusively spied on” and said: “Nothing like this has ever happened in American Politics. A really bad situation. TREASON means long jail sentences, and this was TREASON!”

His opponents say his instruction to Barr to investigate the investigation is a nakedly political move that risks compromising US intelligence. Trump’s own director of national intelligence, Dan Coats, has expressed similar concerns.

We already know that there was an outrageous amount of corruption that took place at the FBI Sarah Sanders

Speaking to NBC from Tokyo on Sunday, White House press secretary Sarah Sanders said Trump “has total confidence in the attorney general and his ability to make those decisions”.

“We already know that there was an outrageous amount of corruption that took place at the FBI,” she claimed. “They leaked information. They lied. They were specifically working trying to take down the president, trying to hurt the president. We’ll leave the final call up to the attorney general and he’ll get to the bottom of it.”

South Carolina senator Lindsey Graham, a close Trump ally, backed the Barr decision.

“I want all the documents around the Fisa warrant application released and [to know] exactly how the counter-intelligence operation began,” he told Fox News Sunday, referring to official surveillance of Carter Page, a Trump adviser with links to Russia.

“I think transparency is good for the American people,” said Graham, who caused controversy himself earlier this month when he advised Donald Trump Jr, the president’s son, to ignore a subpoena from the Senate intelligence committee.

Of Speaker Nancy Pelosi’s caution on the impeachment question, Graham said: “70% of the Democratic base wants President Trump impeached. She knows that impeachment would be political suicide, because there’s no reason to impeach the president. So she’s trying to keep the party intact. If she goes down the impeachment road, Republicans take back the House, we keep the Senate, President Trump gets re-elected.”

Facebook Twitter Pinterest Hakeem Jeffries speaks in Washington. Photograph: Kevin Lamarque/Reuters

For his part, Jeffries called again on Barr to release the full Mueller report and the evidence that underpins it.

“We can’t trust the attorney general’s redactions to be presumptively legitimate,” he said. “We want to see the underlying documentation and of course we’d like to hear from Bob Mueller who needs to tell his story to the American people.”

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Negotiations continue over how or whether the special counsel will testify to Congress.

In dramatic scenes at the White House this week, Trump said he would not work with Democrats on legislation to improve national infrastructure while they are investigating him. Jeffries said the president had not just walked out on a meeting with Pelosi and Senate minority leader Chuck Schumer, but had abandoned the American people.

“Donald Trump is functionally a studio gangster,” he said. “He pretends to be a tough guy but he really is just playing that role on TV. Hopefully he will have gotten this temper tantrum out of his system.

“He can come back from Japan. We have crumbling bridges, roads, tunnels, airports, mass transportation systems. We need to get to work to fix it. We have a plan and we’d like to do it in a bipartisan way.”