House Democrats, after committing to an impeachment vote, now face the task of building support among voters who have been consistently skeptical of the idea of removing President Trump from office.

The country remains split on the question of impeachment and removal despite a steady stream of Democratic leaks from the inquiry’s closed-door hearings that point to wrongdoing by the president in dealings with Ukraine.

In an attempt to move the needle of public opinion, Democrats are set to begin open hearings that will broadcast what they have been billing as damning testimony. As a political strategy, there is no guarantee it will work. Other attempts to use congressional hearings to ding the president, including hotly anticipated appearances by special counsel Robert Mueller and former Trump campaign manager Corey Lewandowski, fell flat.

Rep. Jackie Speier, California Democrat, said the public hearings will start after the closed-door sessions wrap.

“The following week is likely to be when we will start having hearings,” Ms. Speier said.

House Democrats have eight witnesses lined up to testify this week. One of them is John R. Bolton, Mr. Trump’s former national security adviser, though it is uncertain whether he will show up.

The public hearings will potentially give the White House and Mr. Trump’s Republican allies their first opportunity to confront accusers and mount a defense.

They also want to hear directly from the whistleblower who sparked the inquiry with allegations that Mr. Trump threatened to withhold aid from Ukraine unless the leadership launched an investigation of former Vice President Joseph R. Biden, a top contender for the 2020 Democratic presidential nomination.

House Minority Whip Steve Scalise, Louisiana Republican, noted rumblings around Washington that the whistleblower previously worked for Mr. Biden, which, if true, would impugn the whistleblower’s motives.

“There are a lot of questions that haven’t been answered,” Mr. Scalise told ABC’s “This Week.”

House Minority Leader Kevin McCarthy, California Republican, said the first witness for the defense should be Rep. Adam B. Schiff, California Democrat and chairman of the House Permanent Select Committee on Intelligence, who has spearheaded the closed-door probe.

Mr. Schiff previously concealed the fact that his staff met with the whistleblower before the complaint was filed.

“He is the only person who knows who this whistleblower is. He refers to himself as a Ken Starr, [and] Ken Starr testified,” said Mr. McCarthy, referring to the special prosecutor who investigated President Clinton before his impeachment.

Polls highlight Democrats’ halting progress in shifting public opinion.

A Washington Post/ABC News poll last week found that Americans’ views on impeachment were virtually unchanged since the inquiry launched, with 49% saying the president should be impeached and removed and 47% saying he should not.

Popular support is key to enlisting Republican lawmakers in the impeachment cause, especially in the Senate, where the Democrats, if unified, would need 20 Republican votes to remove Mr. Trump from office.

In the House, no Republican crossed the aisle to vote for the impeachment inquiry.

Even if impeachment efforts fall short of removing the president, Democrats are counting on a damning final report, authored by Mr. Schiff, to provide ammunition against Mr. Trump and his Republican allies in next year’s presidential and congressional races.

House Speaker Nancy Pelosi, California Democrat, reassured colleagues in her party over the weekend that they already had enough evidence to impeach Mr. Trump for asking Ukraine to investigate corruption involving Mr. Biden, a political rival.

In a letter to House Democrats, she noted that polls show support for impeachment has risen from the mid-30s before the inquiry to the high 40s.

“I believe that the truth will set us free, and the facts are clear,” Mrs. Pelosi wrote in her clearest signal yet that she already knows the outcome of the inquiry will be an impeachment in the House.

Last week, she described the impeachment inquiry as a fact-finding mission without a predetermined outcome.

The letter spelled out what Mrs. Pelosi said the evidence would show: that Mr. Trump withheld U.S. military aid from Ukraine to force Kyiv to investigate Mr. Biden and his son Hunter.

“Ukraine desperately needed this assistance. At least 11,000 Ukrainians have already died in the fight against Russia’s incursions into their country,” she wrote. “The President’s actions undermined national security, jeopardized the integrity of our elections and violated his oath to preserve, protect and defend the Constitution.”

Mr. Trump responded sharply to Mrs. Pelosi.

“Nancy Pelosi has become unhinged. There is something wrong with her,” he told reporters. “We did absolutely nothing wrong.”

Democratic lawmakers, for the most part, are standing behind the speaker.

Rep. James E. Clyburn of South Carolina, the House’s third-ranked Democrat, said Sunday that he is unsure whether Mr. Trump committed a high crime or misdemeanor worthy of impeachment, but he insisted that Mrs. Pelosi is correct about bipartisan support across the country to impeach Mr. Trump.

“She knows how our Republican colleagues are prone to vote on these issues,” Mr. Clyburn told CNN’s State of the Union. “That is not reflective in this country.”

Leaked testimony, including accounts from State and Defense department officials who expressed concerns about the president’s political motives in dealing with Ukraine, has impacted voters’ views, polls show.

The share of Americans who now believe Mr. Trump asked Ukraine to investigate Mr. Biden has risen to 60% and those who believe he held up U.S. military aid as leverage reached 52%, according to a Fox News poll released Sunday.

More Americans believe the president held up military aid — the quid pro quo at the heart of the Democrats’ impeachment case — than the 49% who say he should be impeached for it, according to the poll.

Americans were split in the poll over removing Mr. Trump from office, with 43% saying it should be decided in the 2020 election and 42% saying he should be removed immediately.

The impeachment inquiry stems from a July 25 phone call in which Mr. Trump asked Ukrainian President Volodymyr Zelensky for the “favor” of looking into allegations of corruption involving Mr. Biden and others.

A rough transcript of the call does not show a quid pro quo, but Democrats argue that the threat to withhold aid was understood and part of an ongoing pressure campaign of “shadow” foreign policy conducted by Mr. Trump’s private attorney Rudolph W. Giuliani.

Testimony provided so far, which has been gleaned from leaked copies of prepared opening remarks and accounts by congressional staff in the room, has largely centered on opinions about what the president was doing on the phone call.

Mr. Trump wanted an investigation into allegations of corruption involving Mr. Biden and his son Hunter, who got a high-paying job on the board of Burisma Holdings, a Ukrainian natural gas company, while his father was the point man for the Obama White House on Ukraine, a country notoriously riddled with graft, especially in the energy industry.

Republicans argue that U.S. law dictates a president must ensure that aid going to a foreign country isn’t diverted to corrupt officials. That justifies the president’s remarks, Republicans say.

Mr. Trump also wanted Ukraine to look into a missing Democratic National Committee server that was hacked by Russia during the 2016 presidential campaigns. An American cybersecurity company called CrowdStrike examined the server to probe the hack, but the server disappeared before it could be handed over to the FBI.

Mr. Trump subscribes to an unsubstantiated theory that the server ended up in Ukraine.

Democratic leaders until last week resisted putting the impeachment inquiry to a vote, saying complaints about the process masked Republicans’ inability to defend Mr. Trump’s action, which they describe as an abuse of his office for personal political gain.

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