At a rally in Davenport, Iowa, on July 28, Republican presidential nominee Donald Trump said he wanted to hit some speakers at the Democratic convention and make their heads spin. (The Washington Post)

Every night here at the Democratic National Convention, the video clips have appeared on giant screens above the arena floor.

“Putting a wife to work is a very dangerous thing.”

“You’re going to have a deportation force.”

“A total and complete shutdown of Muslims in the United States.”

On their biggest stage yet, Democrats have brandished what they think is their most powerful weapon against Donald Trump: his own words. Again and again, Hillary Clinton’s campaign has hurled her Republican presidential rival’s most offensive phrases out into the ether: in flashing videos, in speeches, and even during commercial breaks, in ads in battleground states.

Democratic vice presidential candidate Sen. Tim Kaine mimicked one of Donald Trump's favorite sayings during his speech at the Democratic National Convention. Repeatedly. (Gillian Brockell/The Washington Post)

Campaign officials think the strategy is a no-brainer. Focus groups and public opinion polls show huge swaths of voters turned off by Trump’s pronouncements regarding immigrants, minorities, women and the disabled.

But the tactic carries risk. A lot of people like what Trump says; he emerged from the Republican National Convention in Cleveland last week even with or ahead of Clinton in several polls. Where some critics see behavior unbecoming for a possible president, many voters see a willingness to take on political correctness and upend long-standing norms. It’s the reason they’re behind him.

And Clinton is testing a theory that has been proven wrong before. During primary season, Trump’s Republican opponents were certain that his insult-hurling style would doom his path to the nomination. They were wrong.

Kellyanne Conway, a senior adviser to the Trump campaign and a longtime GOP pollster, said in an interview this week that voters are so upset with the status quo — and so mistrustful of Clinton — that “distrust will trump distaste.”

“Those are the voters who may have once prioritized tone and temperament,” she said.

“Now, their priorities have changed. What’s going on is so bad, the angst is so real, that people are willing to take the chance.”

This video played at the Democratic National Convention on July 27 criticizes Republican presidential nominee Donald Trump for not making good on his promises to donate to veterans' charities. (Democratic National Convention)

Clinton is not trying to change the minds of voters who like what Trump has to say. Rather, it’s to repackage his most incendiary comments for crucial blocs of voters in contested states, so they will be exposed to the words they find most offensive — and motivated to vote against Trump. Democrats say it’s a playbook his Republican opponents haven’t been able to execute.

A recent spot called “Role Model” shows young children watching as Trump jeers and uses profanity on a television screen. It is aimed at suburban families, mothers in particular, who the Clinton campaign thinks are prime targets in this election.

For Latino audiences, no line is more potent, Democrats say, than Trump’s claim that undocumented Mexican immigrants include criminals and rapists.

“My father is not a criminal or a rapist, in fact, he’s a United States veteran,” Latina actress Eva Longoria said Monday night.

Then, minutes after video footage of Trump mocking a disabled reporter played, Anastasia Somoza came onto the stage in her wheelchair.

“Donald Trump has shown us who he really is,” Somoza said. “And I honestly feel bad for anyone with that much hate in their heart.”

An ad from the super PAC Priorities USA, about a disabled woman named Grace, hammered home the same point.

“The children at Grace’s school all know never to mock her,” Lauren Glaros, an Ohio mother whose child has a disability, says in the ad. “And so for an adult to mock someone with a disability, it is shocking.”

There was no subtlety in these messages, and that was the goal. The pitch is straightforward: Trump is who he says he is.

“I don’t think you can find any Republican who can defend some of the stuff that Donald Trump is saying,” said Jamie Harrison, chair of the South Carolina Democratic Party.

The party faithful at Wells Fargo Center here needed no convincing.

“Your word really identifies who you are and what you believe,” said Jeion Ward, 62, a delegate from Virginia and a member of the Virginia House of Delegates. “He wouldn’t really say that if he didn’t believe it, right?”

But Harrison said Democrats are also aiming squarely at moderate voters not in the room, whom Democrats hope will do a double take when confronted with evidence of Trump’s core beliefs.

“It’s for independents and it’s for moderate Republicans who are fiscally conservative but who like to think of themselves as moderate on issues like equality for the LGBTQ community, equal treatment for minorities, people who don’t think that we need a religious litmus test in terms of entrance and exit for our country,” Harrison said.

According to a recent Washington Post-ABC News poll, Clinton ties or leads Trump on issues including trust and temperament. But when it comes to change, Trump has a slight advantage: 46 percent say he would do more to bring about the change needed in Washington, while 44 percent say Clinton would.

John Podesta, Clinton’s campaign chairman, acknowledged that her challenge remains to win over voters who are entertained or intrigued by Trump.

“Some people like it. It works on reality TV,” he said at a Wall Street Journal lunch this week. “But having a temperament that is quick to anger, discounts study, is impetuous, has probably never before been thought of as a qualification for putting your finger on the nuclear codes.

“I think that while it has some appeal to certain people who are entertained by it, I think it’s also quite dangerous,” he added.

The project began in earnest when Clinton delivered a foreign policy speech in early June that was devoted exclusively to deriding Trump’s statements. She mocked the real estate mogul and painted him as unserious and dangerous.

One worry for Democrats is that Trump’s political rise would “normalize” his rhetoric, desensitizing voters to comments or behavior that were once considered out of bounds in politics.

“We have to call out this behavior and his oftentimes racist and bigoted and fascist appeals,” former Maryland governor Martin O’Malley said in an interview at the convention this week.

But he warned that disqualifying Trump “isn’t enough.”

“We have to lay out our story and agenda in a positive way,” he said. “You have to do both: do what’s morally responsible by calling out the opponent so he can’t scapegoat people and vilify, then turn to our issues in a big way.”

Voters may be shrugging off the near-constant attacks on Trump, Republican National Committee spokesman Sean Spicer said.

He said the RNC is ready on several platforms — digital, television, social media — to counter each night’s various criticisms of Trump but doesn’t consider that effort a dominant part of the convention because he is so well-known and few, if any, barbs have become major stories.

“We did some fact check, sure. But we’re looking at the Democrats’ hypocrisy and mistakes and we want to make sure we expose their flaws and their messaging,” he said.