Senate Democrats on Wednesday called for delaying confirmation hearings for Supreme Court nominee Brett M. Kavanaugh in the wake of a guilty plea by Michael Cohen, President Trump’s former attorney, on campaign-finance counts that involve the president.

Democrats, who have been seeking leverage to slow down Kavanaugh’s consideration, argued that a new justice could be forced to decide questions directly relating to Trump, including whether he must comply with a subpoena from prosecutors and whether he can be indicted while in office.

“It is unseemly for the president of the United States to be picking a Supreme Court justice who could soon be effectively a juror in a case involving the president himself,” Senate Minority Leader Charles E. Schumer (D-N.Y.) said during a floor speech. “The prospect of the president being implicated in some criminal case is no longer a hypothetical that can be dismissed.”

The Democratic demands were met with immediate rejections by White House officials and Senate Republicans, who said the ongoing Trump investigation was not connected to the Kavanaugh nomination and that hearings would begin as planned Sept. 4.

“I don’t see a basis for delaying them,” Sen. Susan M. Collins (R-Maine), a key swing vote on the nomination who met the judge this week, said Wednesday.

The Cohen plea agreement, along with the eight-count conviction of former Trump campaign chairman Paul Manafort on tax charges, elicited partisan reactions on Capitol Hill that have remained largely unchanged throughout the Trump presidency and the 15-month-and-counting investigation by special counsel Robert S. Mueller III.

Republicans expressed some level of dismay at the serious nature of the charges and repeatedly called on Trump to avoid any interference in the Mueller probe. “These are serious charges, and they can’t be ignored,” said Sen. Orrin G. Hatch (Utah), who noted that so far the prosecutors have focused on Trump’s advisers. “We’ll have to let it all run out and see what happens.”

But the vast majority of Republicans declined to support any formal action to shield Mueller or fulfill Congress’s oversight role by holding hearings into the new Cohen allegations that Trump himself directed the onetime fixer to make the payments to alleged mistresses to prevent them from going public just before the 2016 election.

Sen. Charles E. Grassley (R-Iowa), chairman of the Judiciary Committee, said he does not believe there is any need to approve the legislation that he passed out of his panel earlier this year that would provide protection for Mueller in the federal courts if Trump tried to fire him.

“I’ve advised just to let the process move forward,” he said of his discussions with White House officials.

“Campaign finance violations are enforced by prosecutors and the Justice Department and the court system, not Congress,” said Sen. Marco Rubio (R-Fla.), a Trump rival in the 2016 presidential primaries.

In fact, congressional Republicans investigated campaign finance improprieties and held months of hearings in 1997 during the Clinton administration.

Incredulous at the lack of action from Republicans, Democrats rushed to cable news and gave Senate floor speeches that raised the specter of impeachment proceedings — but very few uttered the I-word.

“We’re too early in the process to be using these words. What we need to do is gather the information,” Sen. Richard J. Durbin (D-Ill.) said.

Sen. Richard Blumenthal (D-Conn.) issued a rare call for supporting a criminal indictment of Trump, a move that would go against past guidance from the Justice Department that a president cannot be tried criminally while in office. “We should talk about all the remedies. Every single remedy, including indictment of the president, should be on the table,” Blumenthal said.

In the House, Democrats pressed for hearings in the Judiciary Committee, with Minority Leader Nancy Pelosi (D-Calif.) writing to colleagues that it was time “to immediately investigate the president’s relentless assaults on the FBI and the Special Counsel.” Republicans were silent on the request.

Powerless to force action, at least before the November midterm elections decide congressional majorities next year, Democrats settled on a strategy that declared Kavanaugh’s nomination was too tainted to move forward.

“It seems at the very minimum we should be withholding this decision on this Supreme Court nominee until the air is cleared,” said Durbin, a senior Judiciary Committee member and No. 2 in leadership.

Even before Tuesday’s events, Democrats had been skeptical of Kavanaugh’s views on whether sitting presidents can be the subject of criminal prosecutions. The legal developments have raised the stakes on that issue, senators said.

“We have a Supreme Court nominee who’s being pushed through . . . that has said through his writings and his speeches that he does not believe the president should be subject to a criminal investigation,” said Sen. Cory Booker (D-N.J.). “What I want right now when it comes to Kavanaugh is to wait for this Mueller probe to be done.”

In the short term, at least one Democrat said she would cancel a planned one-on-one meeting with Kavanaugh.

“I would choose not to extend a courtesy to a president who is an unindicted co-conspirator, extend the courtesy of meeting his nominee for the Supreme Court,” said Sen. Mazie Hirono (D-Hawaii). “A judge who has been nominated because the president expects him to protect him.”

But other Democrats, including Durbin and Sen. Christopher A. Coons (D-Del.), scheduled their sit-downs with Kavanaugh for later this week.

During a television appearance Tuesday on MSNBC, Sen. Kamala D. Harris (D-Calif.) also referred to Trump as an “unindicted co-conspirator” and said he “should not be in the business of having the ability to appoint someone to a lifetime position on the highest court in our land.”

Some Republicans saw these assertions as just part of the drumbeat toward an attempt at impeachment, if Democrats win back the majority, even though few Democrats have actually advocated any attempt to remove Trump from office.

“They’ve never been happy with the outcome of the election in 2016, and I expect them to continue their campaign to reverse the election by whatever means possible,” Sen. John Cornyn (R-Tex.) said.

Paul Kane, Seung Min Kim and Felicia Sonmez contributed to this report.