GEOFF BENNETT: A recent survey from the Pew Research Center found that more than 40 percent of Trump supporters don't believe next week's election will be run well, despite efforts by lawmakers and election officials to address their concerns since 2020.

Judy Woodruff explores what the gap in election trust may mean, part of her series, America at a Crossroads.

JUDY WOODRUFF: As Americans line up to vote early in person, drop off their ballots, or make plans for Election Day, many officials are bracing for an onslaught of conspiracy theories, protests, legal challenges, and even violence.

JANICE WINFREY, Detroit, Michigan, City Clerk: My concerns are not with the administration and the process.

I'm very confident in that process.

But I am concerned and hopeful that our country will accept whatever the outcome of this election is.

BILL GATES (R), Chairman, Maricopa County, Arizona, Board of Supervisors: But we know that it's not easy, because we know that, unfortunately, people have been fed lies about our election system now for literally four years.

BARTON GELLMAN, Brennan Center for Justice: There have always been a few doubters.

There have always been conspiracy theorists who worried about whether someone was rigging the count.

JUDY WOODRUFF: Barton Gellman is a senior adviser at the Brennan Center for Justice, a nonpartisan think tank at New York University, where he's been studying how to protect democratic norms and institutions.

BARTON GELLMAN: Those were never very large numbers, in part because their political leaders did not validate those false concerns.

That's changed, and it's had corrosive effects on confidence in the electorate.

JUDY WOODRUFF: Gellman is a former Pulitzer Prize-winning journalist who in the November 2020 issue of "The Atlantic" magazine warned that then-President Trump could attempt to subvert the election results to hold on to power.

DONALD TRUMP, Former President of the United States (R) and Current U.S. Presidential Candidate: This is a fraud.

JUDY WOODRUFF: On election night in 2020, Trump claimed victory well before counting had ended.

DONALD TRUMP: We were getting ready to win this election.

Frankly, we did win this election.

(CHEERING) JUDY WOODRUFF: In the days and weeks after, his supporters protested the results through Stop the Steal rallies and dozens of court challenges, virtually all of them rejected on the merits or on questions of standing.

Ultimately, Trump attempted to stop the vote certification January 6.

DONALD TRUMP: We will never give up.

We will never concede.

It doesn't happen.

You don't concede when there's theft involved.

(CHEERING) JUDY WOODRUFF: More than 1,000 people have been prosecuted and found guilty for their actions that day.

In late 2022, Congress passed and President Biden signed the Electoral Count Reform Act, strengthening counting procedures and clarifying roles between federal and state actors.

In a recent cover story for "TIME" magazine, Gellman examined that law and other updates to our electoral system, speaking with officials across the country, including in key battleground states, about whether our voting system will hold up against baseless challenges this time around.

BARTON GELLMAN: I ask election officials in all those states how confident they are that the ballots would be counted as cast, that, when they were canvassed and audited, that the council would hold up and that whoever won the most votes in their states would get that state's electoral votes when it went to Congress.

And all of them said 100 percent.

They really were completely confident.

I found that the system has worked very hard to address the worries that people had about the last election.

It's worked very hard to address the false rumors that were spread or the false accusations that were made about the 2020 election.

JUDY WOODRUFF: According to a recent survey by the Pew Research Center, most Americans do trust that the election will be run well.

But, like many things, that trust now tracks partisan lines.

While nine in 10 Harris supporters told Pew they believe the election will be run smoothly, just over half of Trump supporters agreed.

This is a marked change since 2018, when Pew's data showed high confidence among supporters of both parties' candidates that the midterm elections would be run well.

MAN: As things stand right now, there is a zero percent chance of a free and fair election in the United States of America.

JUDY WOODRUFF: Earlier this year, The Heritage Foundation and the Texas Public Policy Institute, two conservative think tanks, held an event marking the release of their 2024 Transition Integrity Project, a report summarizing exercises they conducted with participants from varied backgrounds to consider scenarios they say could threaten the legitimacy of the election.

The report asserted that the lawlessness of the Biden administration makes clear that the current president and his administration not only possesses the means, but perhaps also the intent to circumvent constitutional limits and disregard the will of the voters should they demand a new president.

ADAM ELLWANGER, Author, 2024 Transition Integrity Project: The main findings are that we have seen an acceleration of lawfare and the weaponization of government institutions that in name should be neutral, but have cast a lot more or less with the Democratic Party.

JUDY WOODRUFF: I spoke this week with the report's principal author, Adam Ellwanger, a professor of English at the University of Houston-Downtown who was a fellow at the Claremont Institute, another conservative think tank.

ADAM ELLWANGER: I think that the American people may be tempted when we hear Kamala Harris saying that Trump is a fascist, that this is literal Hitler, I think normal Americans are tempted to think, oh, this is exaggeration.

I think that we need to take them at their word.

And if you believe that a literal Hitler is poised to take over the government of the United States of America, you will not honor that result.

JUDY WOODRUFF: For the record, Harris has said she believes Trump is a fascist, but did not call him Hitler.

The report did not mention the events of the last presidential election, or President Trump's refusal to say he would accept the election results in 2016, 2020, or in the run-up to this current election were he to lose.

In each of the two scenarios they considered, Trump won.

The project did contemplate some unusual hypotheticals, like Barbra Streisand being kidnapped by Hamas militants and the FBI arresting Trump at Mar-a-Lago two days after winning the election.

ADAM ELLWANGER: Well, I think that especially the last 10 years of American life in politics has been defined by scenarios that we could not have anticipated in real life.

If we said that we would see a presidential administration doing an armed raid of a former president's residence, I think we would have said that's preposterous.

That will never happen in America.

And so for these reasons, we decided that we needed to really test the system by running scenarios with events that would be highly unanticipated.

JUDY WOODRUFF: Ellwanger also questioned whether Harris, in her role as vice president, will certify the election results in the Senate should President Trump win.

The Electoral Count Reform Act clarified that this is a ceremonial duty.

ADAM ELLWANGER: Will Kamala Harris do a transfer of power when she oversees a joint session of Congress?

Nobody's asked her, so we don't know.

JUDY WOODRUFF: Vice President Harris has been asked if she would respect the results of the election, whatever they are, and she said yes.

So she has been asked those questions, and she has said that she would respect the results whatever happens.

As you know, former President Trump, so far, he has not said he would accept the results of the election.

ADAM ELLWANGER: Is there a question in there?

JUDY WOODRUFF: I'm asking -- I'm saying -- I'm pointing out you just said that she hasn't been asked or she hasn't said this.

And she has said.

ADAM ELLWANGER: If you would like a response to that, I would say she said lots of things and then changed her mind after the fact on virtually every issue.

JUDY WOODRUFF: He also warned that, if results aren't known on Election Day, they should be questioned.

A critic would say this report looks like a pretext in case former President Trump loses the election for people who support him to say there was something wrong and this is going to -- and this lays out what's going to happen.

Is it a pretext, in so many words?

ADAM ELLWANGER: I don't think it's a pretext.

I do think that many of the fantastical situations that we imagined have already occurred.

I invite your viewers to read the report.

Things that only three months ago people were saying, well, that won't happen, has already happened.

JUDY WOODRUFF: As an example, he pointed to ongoing conservative efforts in a number of states to prevent noncitizens from voting, including through purging names from voter rolls whom they suspect don't have citizenship, which the Department of Justice has sued to block as a violation of law.

This week, the Supreme Court ruled that Virginia's purge of 1,600 names could go forward, despite the fact that officials there haven't proven any of the names actually lack citizenship and some U.S. citizens said they had been removed.

Stepping back, it is illegal for noncitizens to vote in federal elections and studies have found almost no cases of it happening, despite The Heritage Foundation and other groups continuing to assert that it's an issue.

ADAM ELLWANGER: Judy, I mean, this in all respect, all due respect, but you keep citing that these institutions have said there's no evidence of this or that, right?

The problem here is, is that they have said this so many times where there is evidence of this or that that's later proven, or where they have said that there is evidence of this or that, say, Russian collusion or a lab leak with COVID, right, where we later found out, when they said that there was no evidence that there was, we simply feel like we can't trust these institutions anymore.

BARTON GELLMAN: What Heritage is doing with that exercise is to amplify what Donald Trump himself is doing, which is to try to convince the public that our election is going to be corrupt, that you cannot count on the institutions of democracy to run a fair election.

JUDY WOODRUFF: Returning to his own reporting, Barton Gellman says Americans should feel confident that official results will accurately reflect the outcome, but that getting to the result will also require patience.

BARTON GELLMAN: What's going to happen is that the votes will be counted.

You will get unofficial results early.

Then over a period of days, and in some cases over a week, you will get a canvassed, audited, verified official result.

And that's when litigation will be coming into play.

If Trump loses, he's going to try to overturn the election.

And the system, I am confident, will block him.

And the public should have confidence that, when the system says who won the election, that that tally is accurate and secure.

JUDY WOODRUFF: Words of confidence and trust in a country where those are becoming rarer and more partisan notions.

For the "PBS News Hour," I'm Judy Woodruff in New York.