GEOFF BENNETT: At a time of intense polarization across the country and bitter partisan battles in Washington, some of the nation's governors are attempting to find a way forward to solve their own state's problems.

Judy Woodruff recently sat down with two governors from opposing sides to talk about their call to disagree better.

It's part of her ongoing series America at a Crossroads.

GOV.

ERIC HOLCOMB (R-IN): Hello.

I'm Eric Holcomb, Republican governor of Indiana.

CLINT LAMB (D), Former Mayor of Sullivan, Indiana: And I'm Clint Lamb, Democratic mayor of the city of Sullivan.

JUDY WOODRUFF: Republican and Democratic leaders sitting down for a meal.

GOV.

MIKE PARSON (R-MO): And like any good neighbor, we will continue to disagree on plenty of things.

GOV.

LAURA KELLY (D-KS): Like barbecue, tax policy, or who's the bigger Chiefs fan.

JUDY WOODRUFF: Encouraging Americans to engage in respectful dialogue.

GOV.

WES MOORE (D-MD): But we can have our differences without being divisive or hateful.

JUDY WOODRUFF: This series from the National Governors Association is the brainchild of NGA President Spencer Cox.

GOV.

SPENCER COX (R-UT): You and I probably disagree on a few things.

And that's OK. JUDY WOODRUFF: The first-term Republican governor from Utah wants to show Americans how to disagree better.

GOV.

SPENCER COX: Our country is deeply divided.

And most Americans are tired of the division.

We see dysfunction in Congress.

We see this deep polarization that's happening all across the country.

And so we had this crazy idea that we could focus on disagreeing better, reminding Americans how to disagree without hating each other and how to try to actually find solutions to some of our biggest problems.

JUDY WOODRUFF: Last week, as governors from across the country gathered in Washington for their winter summit, I met Governors Cox and Wes Moore, the first-term Democrat from Maryland, at an event hosted by the Economic Club of Washington to talk about why they're pushing this initiative now.

GOV.

SPENCER COX: It's been a fantastic opportunity for us to remember that there's nothing more un-American than hating our fellow Americans.

GOV.

WES MOORE: We are not going to get anything done if we just simply scream into a wind or if we're just talking to an echo chamber.

Our ability to be able to be productive, our ability to be able to be effective means that we have to work across the aisle.

It means that we have to be able to meet with people who, even if you at the end of the process disagree with the conclusion, they will at least respect the process, that you heard them, that they understood where you came from, and that you understood where they came from.

JUDY WOODRUFF: Governor Moore, I want to ask you about how you work through some of the most difficult, most divisive issues of our time.

One of them is immigration.

What's an example of a way to even talk about immigration that would be productive?

GOV.

WES MOORE: Yes.

I think the thing that we can all fundamentally agree to is that the system that we have in place right now, it does not work.

And so the reason that I signed a letter with eight other governors saying that we are urging Congress to move on this, what was so frustrating watching a bill that was literally worked on with the president, Democrats, and even conservative Republicans, like Senator Lankford, to go down in flames, why it was so frustrating is that the consequences fall on our shoulders.

And that's why we need a measurement of action.

JUDY WOODRUFF: So could you, Governor Cox -- you're a Republican.

You have seen what's happened.

You heard -- you know that it's the Republicans in the House who are saying, we're not going to go along with this.

What's a way through this?

GOV.

SPENCER COX: Well, the way through is, unfortunately, we need Congress to start doing their job and the president to enforce the laws.

Those -- it's really that simple.

This is the least divisive of the most divisive issues.

If you poll Republicans and Democrats, everyone agrees.

They just do.

Democrats believe we need to secure the border and Republicans believe we need to fix illegal immigration.

I can tell you right now, if Governor Moore and I were asked to solve this problem, even if you just had all 50 governors solve this problem, we could sit down and do it in a weekend.

JUDY WOODRUFF: Of course, there are real and substantive differences over how to move forward on divisive issues like reproductive rights, transgender policy, and diversity, equity and inclusion initiatives.

Just recently, Governor Cox signed legislation in Utah banning DEI programs in state government and universities, prohibiting gender-affirming care and surgery for minors, and mandating that trans people use the bathrooms that correspond with their gender assigned at birth in public schools and state-owned buildings.

Both Cox and Moore emphasize that disagree better doesn't mean there won't be real disagreements at the end of the day.

GOV.

SPENCER COX: The process matters.

I think the process is really important and the way we treat each other.

And the way we have approached DEI is a little different than other states.

We're trying to focus on government not discriminating on the basis of color, but helping everyone who's struggling.

We want everyone to feel included.

We think inclusiveness is very important.

We think diversity is very important.

And how we do that, how we use the power of the state to do that is also really important.

And that's where there is definitely some disagreement.

Sometimes, too much gets lumped into DEI that really isn't DEI.

And understanding what the philosophy is behind it is really important.

And so, yes, there are major disagreements when it comes to DEI, but, at the end of the day, I think we're seeking the same thing.

And that is that everyone feels included, that everyone has the same opportunity, that we're -- the deck is not stacked against anyone.

That really matters to me and I think it matters to most Americans.

GOV.

WES MOORE: And I think there - - that's exactly right that we want to make sure that everyone is just getting a fair shot at open success.

We know that a lot of the discrepancies and a lot of the disparities that we have seen in our society, that we still see to this day, everything from wealth gaps, to housing gaps, to educational gaps, they haven't been by accident.

There have been government policies that have helped to create that.

The reason that we look at things like a racial wealth gap, for example, you can't understand that without understanding things like the Homestead Act, the unequal application of the G.I.

Bill, historic redlining.

You can't understand how the racial wealth gap has ballooned to 10-1 in this country without understanding that it's been government policies that have helped to create that level of gap.

What is government's role to help to address the inequities that government helped to create?

GOV.

SPENCER COX: I'm Spencer Cox, your Republican candidate for Utah governor.

CHRIS PETERSON (D), Former Utah Gubernatorial Candidate: And I'm Chris Peterson, your Democratic candidate for governor.

JUDY WOODRUFF: Yet another issue starkly dividing the country is trust in elections.

In 2020, as he ran for his first term as governor, Governor Cox joined his Democratic competitor in a pledge to honor the outcome of the election, whatever the results.

CHRIS PETERSON: And whether you vote by mail or in person, we will fully support the results of the upcoming presidential election, regardless of the outcome.

JUDY WOODRUFF: Researchers at Stanford studying polarization told me last year that this kind of public act by leaders can make a real difference in ratcheting down partisan animosity.

And yet, right now, the latest poll shows 69 percent of Republicans say they don't believe Joe Biden legitimately won the election in 2020 to be president.

How do we move forward when there's a disagreement on something as fundamental as that?

GOV.

SPENCER COX: Yes, that's a tough one, for sure, there's no question.

And I'm very fascinated about how and why that's been able to happen, that myth has been perpetuated so much, when we have had legal proceeding after legal proceeding that has shown that none of those allegations were true.

And it's difficult in this new era, where we have social media and we can surround ourselves with information that just confirms whatever we want to believe, our biases, instead of actual truth and seeking for truth.

And that deeply concerns me as a nation.

We need good people who are willing to stand up and speak the truth, even if it's unpopular.

And I will certainly continue to do that.

GOV.

WES MOORE: I ran against an election denier, where, when asked the question, would he accept the results of the election, his answer literally was, it depends on the results of the election.

And so it's a very difficult baseline.

Let's just start that conversation with that.

But I think the thing that we continue to have to do is understand why that exists.

And for a lot of people, it is a lack of trust.

It's a lack of trust in institutions.

That statistic is something -- it's actually saying something much bigger.

It's not just about elections.

It's not about an election.

Do we trust our institutions to actually make our lives better?

JUDY WOODRUFF: You're all about trying to get people to listen to the other side.

And yet the person who is the likely Republican nominee for president this year is someone who seems to pride himself, Governor Moore, on being a divider, rather than a uniter.

And that is former President Trump.

How do you do this work under those circumstances?

GOV.

WES MOORE: Because I'm not doing this work because I'm pushing against Donald Trump.

I'm doing this work because there was over a million Marylanders who said, we want you to do the job and remember us.

I don't get up in the morning and think to myself, what do I have to do to combat the ills of Donald Trump, or his vitriolic language, or the absurdity of some of the things that he says on a repeated basis.

I'm doing this work because there are 6.3 million people who are asking me every single day to remember them, not him.

GOV.

SPENCER COX: When we elevate kind of a single election, it leads to more problematic behavior.

If this really is the most important election in the history of the United States, then every side should be doing everything possible to win, even if it's maybe not legitimate, right?

And that's a dangerous way to look at things.

Our country is bigger and better than any single person or any single president.

We have 50 states, 50 states where we're innovating, where we're stealing ideas from each other, where we're fixing actual problems.

America is so much better and more resilient than Joe Biden or Donald Trump.

And thank goodness we are because that's how we have made it through the last eight years and it's how we're going to make it through the next four no matter who gets elected.

And so I just -- I believe in us.

I believe in the American people, and I believe that we should be engaging with the American people to find out why they feel so attacked all of the time and to try to make life better for them.

JUDY WOODRUFF: A call to all Americans to focus on finding solutions, compromise and listening to each other.

For the "PBS NewsHour," I'm Judy Woodruff in Washington.