GEOFF BENNETT: Today, President Biden and former President Trump made separate visits to two towns along the southern border, as immigration becomes the key issue ahead of the November election.

Laura Barron-Lopez has been reporting from Brownsville, Texas, on the president's trip.

LAURA BARRON-LOPEZ: In his second visit to the Texas-Mexico border, President Biden met with Border Patrol and immigration officials in Brownsville, attempting to turn the tables on his likely 2024 rival, former President Donald Trump.

JOE BIDEN, President of the United States: Here's what I would say to Mr. Trump.

Instead of telling members of Congress to block this legislation, join me, or I will join you in telling the Congress to pass this bipartisan border security bill.

We can do it together.

You know and I know it's the toughest, most efficient, most effective border security bill this country has ever seen.

LAURA BARRON-LOPEZ: Meanwhile, some 300 miles West along the Rio Grande in the town of Eagle Pass, Trump attacked Biden and again demonized migrants.

DONALD TRUMP, Former President of the United States (R) and Current U.S. Presidential Candidate: Now the United States is being overrun by the Biden migrant crime.

It's a new form of vicious violation to our country.

It's migrant crime.

We call it Biden migrant crime.

LAURA BARRON-LOPEZ: The showdown here at the U.S.-Mexico border is set to be a defining battle of 2024, a fight guaranteed when Republicans killed a bipartisan deal designed to stem the flow of migrants and funnel billions to border security.

What do you hope President Biden's trip accomplishes?

CHRIS CABRERA, Vice President, National Border Patrol Council: You know, hopefully, he takes some good out of this trip, and, hopefully, when he meets with the Border Patrol agents, they give him an idea of what you could work from.

Any time you want something done on the front line, you need to talk to the front-line workers.

LAURA BARRON-LOPEZ: Chris Cabrera is the vice president of the National Border Patrol Council, a union representing 18,000 agents nationwide.

The union supported the bipartisan deal.

Do you want it to still pass?

CHRIS CABRERA: You know, that's the hope.

But on top the -- at the end of the day, anything will help.

I know there's the power of the pen.

There's executive action that he's done in the past with other issues.

He has the power to put a stop to this today if he wanted to.

Granted, Congress does have some fault in this.

They have been kicking the can down the road for quite a few years, not one side or the other, but both sides.

And if they're not going to do it, then either we get somebody in there that will or the president needs to take action like the last president did.

LAURA BARRON-LOPEZ: With the Senate deal all but dead, sources have told "NewsHour" that President Biden is considering using his executive authority through a decades-old law to block some asylum seekers from entering the U.S.

While state and federal authorities clash in Eagle Pass, becoming a national flash point, here in Brownsville, advocates say things are different.

ASTRID DOMINGUEZ, Executive Director, Good Neighbor Settlement House: We often hear that the border is chaotic, but it's orderly.

It's not chaos.

LAURA BARRON-LOPEZ: Astrid Dominguez is the executive director of Good Neighbor Settlement House, which is one of the groups that helps welcome asylum seekers in Brownsville.

What would the impact be for migrants if the U.S. were to put in place more severe asylum restrictions?

ASTRID DOMINGUEZ: Seeking asylum, it's a right.

And we want to make sure that, as a country, we're looking at solutions that allow them to seek asylum in a safe way and not putting them in danger.

LAURA BARRON-LOPEZ: Despite the danger, some are still making the long journey with their children.

Roxanna just arrived from Cuba.

ROXANNA, Asylum Seeker From Cuba (through translator): It was difficult because we had to travel with coyotes and we had a small child.

LURIA, Asylum Seeker From Venezuela (through translator): I cried a lot.

It was terrifying.

I'm 22 years old.

I don't know how I did it, how I was able to flee with my son.

It's something that I just don't know how I did it.

But I accomplished it, and we're here, and that's the most important thing.

LAURA BARRON-LOPEZ: Fleeing Venezuela through the Darien Gap, 22-year-old Luria was robbed twice before arriving for her appointment with Customs and Border Protection.

LURIA (through translator): I want a better life.

I want a better future for my son, and I just want to start a new life.

LAURA BARRON-LOPEZ: Geoff -- Geoff, those migrants are arriving through the CBP One appointment system app that President Biden has urged asylum seekers to use, rather than cross regularly into the United States.

But, overall, Geoff, crossings are low here right now in Texas.

GEOFF BENNETT: And, Laura, let's return to what we heard today from the current and former presidents.

We heard Donald Trump with his criticisms of Joe Biden.

How do Mr. Trump's stated concerns and contentions square up with the facts and with your reporting and what you're seeing there along the border today?

LAURA BARRON-LOPEZ: Geoff, Chris Cabrera of the Border Patrol union told me that there were only six apprehensions in Brownsville yesterday and that overall, across Texas, other entry points, other border towns may have slightly higher apprehensions, but that it's overall low.

But I want to point out, Geoff, and fact-check one of the things that the former president said today.

He was talking about claiming that there was a migrant crime wave occurring.

And the data just doesn't match up with that, Geoff.

A Stanford study shows that immigrants are 60 percent less likely than native-born Americans to be incarcerated and that also, in sanctuary cities, each unit increase in the unauthorized immigration population actually represents a 5 percent decrease in violent crime.

GEOFF BENNETT: And President Biden today, he also called on Senate Republicans to pass that bipartisan border deal, but he said he might act alone.

There's word of an executive order?

Is that right?

Tell us more about that.

LAURA BARRON-LOPEZ: That's right, Geoff.

An executive order could come in a matter of weeks.

And that order, what's being considered right now would severely restrict asylum seekers.

It would narrow who can claim asylum.

And I was talking to immigration advocates today who have been in talks with the White House.

And they're trying to convince President Biden to essentially go a different route with an executive order, declare an emergency declaration, and just send more resources border, rather than restrict asylum.

It's important to note, Geoff, that asylum under current U.S. law is a right for migrants to claim whether they're presenting at a port of entry or between ports of entry.

GEOFF BENNETT: In the meantime, Laura, there is this continuing dispute between Texas and the federal government over border security.

Where does that stand right now?

LAURA BARRON-LOPEZ: A federal judge today, Geoff, blocked a Texas law that would give police more authority to arrest migrants that they suspect may have entered into the U.S. illegally.

And I was speaking with an immigration lawyer today who said that they expect Texas will ask for a stay, which would allow them to try to implement that law as legal proceedings move forward.

But, of course, they're going to be battling with immigration lawyers and advocates who are trying to block this to take effect.

And one thing that's important to note, Geoff, is that a lot of people can't always present at a port of entry when they're trying to come into the U.S.

There's a lot of reasons why they actually present between ports of entry, as they're trying to flee violence.

And I also spoke with a lifelong Texan today in Eagle Pass, Geoff.

He's a business owner who's been really frustrated by Governor Greg Abbott's Operation Lone Star, saying that, initially, he supported it, but that now he isn't really happy with what's been going on, because Governor -- the governor has seized so much of the land and so much of the public property in Eagle Pass.

GEOFF BENNETT: Laura Barron-Lopez on the U.S. southern border for us tonight.

Laura, thank you.