They impeached him. They are still trying to remove him. They’re vowing to continue investigating him.

And on Tuesday, prominent Democrats made clear they don’t see much potential for finding common ground with President Trump, brushing aside his offer of outreach at his State of the Union address.

House Speaker Nancy Pelosi literally tore her copy of the speech apart at the end of Mr. Trump’s remarks.

Other Democrats said they couldn’t even bear to be in the same room with him.

Powerful committee chairwoman Rep. Maxine Waters, California Democrat, said she was sitting it out. Rep. Alexandria Ocasio-Cortez boycotted, saying she didn’t want to “normalize” the president’s behavior by lending her presence to his speech. So did Rep. Ayanna Pressley, and Rep. Bobby Rush.

“It would be painfully hypocritical of me to endure 90 minutes of unrelenting lies and all types of distortions and untruths, while at the same time watching his Republican apologists cheer,” said Mr. Rush, Illinois Democrat. “I cannot honor this man in any way.”

Rep. Tim Ryan, Ohio Democrat, announced he walked out of the speech, calling it “all fake.”

Mr. Trump became the second president to deliver an address to a joint session of Congress while under the cloud of impeachment. The cloud should be lifted Wednesday, when a majority of senators are expected to vote to acquit him on both articles.

Yet that will do little to patch a relationship that was broken even before Mr. Trump took office, and that despite some rays of sunlight over the last three years has generally been as gloomy as any time this side of the Civil War.

Mr. Trump ignored the impeachment, but for Democrats it was all-consuming.

“We heard a lot of words from the president tonight, but his actions demonstrate his complete disregard for the rule of law and for the principle that no one is above the law, including the president of the United States.”

Rep. Veronica Escobar, delivering Democrats’ official Spanish-language response, insisted the case against the president was sound, despite an expected majority vote Wednesday to reject it.

“We know that President Trump violated his oath by asking for foreign interference, jeopardizing the integrity of our elections, putting our national security at risk, and then attempting to cover up his wrongdoing,” she will say. “This is a tragic moment, and Congress must defend our republic.”

Michigan Gov. Gretchen Whitmer, in the English-language response, attempted to deflate Mr. Trump’s election-year victory lap on the economy, saying as good as the numbers are, that’s not touching average Americans.

“It doesn’t matter what the president says about the stock market. What matters is that millions of people struggle to get by or don’t have enough money at the end of the month after paying for transportation, student loans, or prescription drugs,” she said.

Her state was one of three key Rust Belt flips Mr. Trump orchestrated in the 2016 election, delivering the White House to Republicans. The others were Pennsylvania and Wisconsin.

Ms. Whitmer pointedly said workers are “hurting” in all three states — and Ohio, too.

The different approaches — Ms. Escobar’s combative rhetoric and Ms. Whitmer’s more policy-centered remarks — underscore the challenge for Democratic leaders, who must find ways to keep both sides happy.

Sen. Jon Tester, Montana Democrat, told reporters it was on Mr. Trump to find a way to bring the factions together.

Sen. Maria Cantwell, Washington Democrat, suggested a good place to start would be for Mr. Trump to tackle election security — which would be an implicit acknowledgement that meddling occurred in 2016.

“We should go to bipartisan fashion to election security issues,” Ms. Cantwell told reporters.

Yet even as they called on Mr. Trump to work with them, House Democrats vowed more investigations.

Oversight Committee Chairwoman Carolyn Maloney of New York said her panel is still probing the president’s abandoned effort to ask about citizenship on the 2020 census.

Speaking before the speech, Mrs. Pelosi had said there was room to work with Mr. Trump — as long as he ditches his agenda.

Chief among her complaints Tuesday was an administration-backed lawsuit that has the potential to undermine Obamacare, and a new Trump proposal to restructure federal payments to states for Medicaid, the government’s health program for the poor.

“Democrats will fight this plan and stand strongly against every last one of the president’s attacks on families’ health care,” Mrs. Pelosi said.

Yet her attempt to focus on policy was in danger of being drowned out by her ripping up the speech, and her party boycotters.

Some Democrats boycotted past Trump addresses to Congress, but this year’s contingent appears to be the largest yet.

White House press secretary Stephanie Grisham called the boycotters “just sad.”

“I think that everybody should be there to support their president and to support their country and the success of this country,” she said in an appearance on Fox News.

Ms. Ocasio-Cortez, who attended last year’s speech, took to Twitter to wonder about all the attention on her decision.

“For Republicans who allegedly ‘don’t care at all’ about us not attending the #SOTU, they sure do seem to have a lot to say about it,” she said.

While most Democrats felt Mr. Trump transformed the national address into a formal campaign rally, a few were still hopeful there could be room to get something done across the political divide.

Throughout his speech, a handful of moderate Democrats from swing districts, including Reps. Max Rose of New York, Abigail Spanberger of Virginia and Elissa Slotkin of Michigan, joined Republicans in applauding the president for some of his economic achievements and even the newly established Space Force.

The opioid crisis and infrastructure are two of the biggest hopes to get bipartisan legislation enacted.

“I think that is a little dispassionate,” Rep. Madeleine Dean of Pennsylvania said. “We can take out all the tensions and anxieties and just say this is about building stuff for the future of this country. I hope we can get there.”

However, other Democrats, including Majority Leader Steny Hoyer, were skeptical that the president would follow through on any of these issues given he’s nearly done with his first term in office.

• Gabriella Muñoz contributed to this article.

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