ON THE U.S.-MEXICO BORDER -- Verlon Jose is vice chairman on the Tohono O’odham Nation -- a tribe of American Indians allowed to cross the border where most Americans cannot.

“I can go, but you can’t go,” Jose told CBS News.

Verlon Jose, vice chairman on the Tohono O’odham Nation CBS News

“We can cross with our tribal IDs,” Jose said. “If you cross, you have to go to an official point of entry.”

The Tohono O’odham Nation is roughly the size of Connecticut. It straddles 62 miles along the U.S.-Mexico border in Arizona.

Tribal members live on both sides and are caught in the middle of the border debate.

They allowed the federal government to build a vehicle barrier in 2006, but they strongly oppose a wall through their land.

The current border fence cuts right through a ranch owned by a tribal family. Their well is now on the Mexican side and a wall would make it impossible to get to.

CBS News

Jose explained how the situation would unfold in his view.

“If I were to go to your home and say, ‘you know what … I should build a wall from your home to your backyard and you can’t cross to your backyard unless you come through me,’” he said.

Sheriff Mark Lamb says illegal immigrants and smugglers come out of the reservation into his county in Arizona, 80 miles north of Mexico. Nearly 3,500 illegal border-crossers were detained in the first month of this year.

We asked Lamb what would happen if a wall were put up on each side of the reservation.

“It’s probably going to increase the traffic coming through the Indian reservation,” Lamb said.

But does he think the wall will work in his opinion?

Sheriff Mark Lamb CBS News

“I do,” Lamb answered. “It’s a deterrent. A lot of people think that’s insensitive. It’s not. We are protecting this great country we live in.”

We asked Jose if this was a battle between Mexico and America.

Jose said, “This is technically ‘Autum hajewet,’ which translates to ‘the people’s land.’”

And since the federal government gave control of this land to the Tohono O’odham more than 150 years ago, it will now require an act of Congress to take it back and build a wall.

Meanwhile, the Department of Homeland Security sent a statement to CBS News: