A surge of reports Sunday about more whistleblowers stoked the Democratic Party’s impeachment momentum, even as Democrats sought to stave off rising Republican calls for a formal House vote and tried to deflect attention from former Vice President Joseph R. Biden.

Andrew Bakaj, lead attorney for the first anonymous whistleblower behind a complaint with the intelligence community inspector general, said his legal team now represents “multiple whistleblowers” related to President Trump’s dealings with Ukraine.

“IC WHISTLEBLOWER UPDATE: I can confirm that my firm and my team represent multiple whistleblowers in connection to the underlying August 12, 2019, disclosure to the Intelligence Community Inspector General,” Mr. Bakaj tweeted. “No further comment at this time.”

Attorney Mark Zaid tweeted that a second whistleblower had direct, “first hand knowledge” of the July 25 phone call between Mr. Trump and Ukrainian President Volodymyr Zelensky, unlike the first whistleblower, who filed the complaint based on secondhand information.

Rep. James A. Himes, Connecticut Democrat, said the emergence of additional whistleblowers is a sign that officials in the executive branch are finally declaring, “My God, this cannot happen anymore.”

“The president’s real problem is that his behavior has finally gotten to a place where people are saying, ‘Enough,’” Mr. Himes, a member of the House Permanent Select Committee on Intelligence, said Sunday on the CBS talk show “Face the Nation.”

If Republicans were worried about the specter of more whistleblowers, they didn’t show it. Sen. Lindsey Graham, South Carolina Republican, said it reminded him of the drumbeat of 2018 sexual misconduct allegations against now-Supreme Court Justice Brett M. Kavanaugh. None of the allegations was proved.

“What did we learn in Kavanaugh?” Mr. Graham asked on Fox’s “Sunday Futures.” “That they were coaching witnesses and they were piling on to try to create an impression that Judge Kavanaugh was a flawed human being. This is Kavanaugh all over again.”

On Twitter, Mr. Trump accused the “Deep State” of “going to the bench” to bolster the first whistleblower complaint, which had been dinged by allegations that the anonymous intelligence official reached out first to the House intelligence committee.

“It doesn’t matter how many people decide to call themselves whistleblowers about the same telephone call — a call the president already made public. It doesn’t change the fact that he has done nothing wrong,” White House spokeswoman Stephanie Grisham said in a statement.

The impeachment inquiry centers on Mr. Trump’s request for Ukraine to investigate Mr. Biden’s involvement with the business dealings of his son Hunter Biden, who gained a seat in 2014 on the board of a Ukrainian energy company despite having no apparent experience in the field.

Democrats have accused Mr. Trump of pressuring a foreign power to dig up dirt on a political rival by threatening to withhold military aid. The president has insisted he imposed no conditions and pointed to a transcript of the conversation released by the White House.

“The reason he had very legitimate concerns and reservations about Ukraine was first, corruption — generalized, it’s endemic, we all know that — and then specifically about election interference in the 2016 election,” Sen. Ron Johnson, Wisconsin Republican, said on NBC’s “Meet the Press.”

At the same time, the query has inadvertently put the spotlight on Mr. Biden, who bragged in 2015 about getting a Ukrainian prosecutor fired by threatening to withhold aid.

“Somebody needs to look at the Bidens, whether or not they violated the law,” Mr. Graham said. “They sure as hell looked at the Trumps. Somebody needs to look at the Bidens.”

Asked whether she would want her hypothetical vice president’s child to sit on a foreign board, Sen. Amy Klobuchar, Minnesota Democrat, said she would not, but “that is not the issue.”

“There’s no evidence that the vice president did something wrong here,” Ms. Klobuchar said on CNN’s “State of the Union.” “What really matters is that the president was repeatedly trying to get dirt on a political opponent. That is the issue here.”

At the Service Employees International Union gathering Friday, Mr. Biden told reporters asking about his involvement in Kyiv politics during his vice presidential tenure to refocus on Mr. Trump.

“There’s been no indication of any conflict of interest from Ukraine or anywhere else, period. I’m not going to respond to that,” Mr. Biden said. “Let’s focus on the problem. Focus on this man, what he’s doing, that no president has ever done, no president.”

The White House was expected to send, possibly Monday, a letter to the House Democratic leadership saying it would refuse to cooperate with subpoenas unless the House formalizes the impeachment inquiry with a full-chamber vote, which House Speaker Nancy Pelosi has avoided.

House Minority Leader Kevin McCarthy, a California Republican who called last week for the inquiry to be suspended, said the process has been shrouded in uncertainty and unfairness by, for example, allowing the majority Democrats but not minority Republicans to issue subpoenas.

In addition, the inquiry is being run by the House intelligence committee — led by Rep. Adam B. Schiff, California Democrat and a key figure in the whistleblower complaint — instead of the House Judiciary Committee, meaning the proceedings may be held in secret.

“Anytime we’ve moved forward with impeachment, we had a vote of all of the Congress. Why? Because America lends their voice to 435 members,” Mr. McCarthy said on Fox’s “Justice with Judge Jeanine.” “They should have a say in their process to start it.”

Mrs. Pelosi and other Democrats have argued that the Constitution does not require her to gain the support of the House but said she would have the votes to authorize an impeachment inquiry if she did bring such a resolution to the floor.

“If Speaker Pelosi did in fact move forward with a floor vote on actually proceeding with an investigation, which as you point out is not required here, there’s no question in my mind that she would have the votes,” Mr. Himes said.

Rep. Eliot L. Engel, New York Democrat and chairman of the House Foreign Affairs Committee, accused Republicans of “throwing things into the mix to say, ‘Well, the Democrats should do this, the Democrats should do that.’”

“What we should all do is make sure that the integrity of our election stands and that the president isn’t taking something that’s not his to barter with in trying to get goods on Joe Biden’s son that he would withhold,” Mr. Engel said.

Meanwhile, Mr. McCarthy blamed politics for the House speaker’s reluctance to call a vote.

“She has 31 current members who are Democrats who sit in seats that Trump carried,” Mr. McCarthy said. “She’ll sit out there and say Republicans are worried. I’m very clear with her: I tried to bring it to the floor twice, and she tabled that vote every time because she’s trying to protect her members and have it both ways.”

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