At the southern border, a group says it's moving ahead with plans to build a private border wall in southwestern New Mexico. It's using millions of dollars from a crowdfunding campaign to close a border gap that the group says is popular with asylum seekers.

Local officials say the project lacks the necessary permits, and issued a cease-and-desist order on Tuesday, though crews plan to continue working around the clock to complete it by the end of the week.

The group known as "We Build the Wall" declared victory, saying they're now effectively protecting a popular passage the immigrants use to enter the U.S. illegally.

"It was a highly trafficked area," Brian Kolfage said, looking at the wall. The project is being spearheaded by Kolfage, a triple amputee veteran. He created the GoFundMe page that has raised more than $23 million.

"How much money is being spent on this section here?" CBS News' David Begnaud asked.

"This one, it's still ongoing but it's going to be around six to eight million dollars," Kolfage responded, sitting in front of the wall.

CBS News reporter David Begnaud interviews Brian Kolfage, a triple amputee veteran who heads the "We Build The Wall" private border wall construction group.

Kolfage is as controversial as the wall. In fact, on Wednesday a Miami radio station reported Florida's Department of Agriculture confirmed the state is investigating the fund after receiving consumer complaints.

"So what do you say to the critics?" Begnaud asked him.

"If we were doing anything wrong, GoFundMe would shut this down in a heartbeat," Kolfage responded.

"Who does manage the money that's been donated?"

"We have an internal audit committee and we have an external audit agency and we can't spend any money without getting approval," he said.

Kolfage later corrected himself and said the group has not yet hired an external audit agency but plans to do so before the end of the tax season.

The wall is being built on privately owned land with permission from the owner and is backed by people like Steve Ronnebeck, who says his son, Grant, was murdered by an illegal immigrant.

"I represent every victim of illegal alien crime," Ronnebeck said.

The plan has faced criticism from city officials. Tuesday, the mayor of Sunland Park, New Mexico ordered the group to stop their work.

In a May 24, 2019 photo, a construction worker watches a section of fencing be moved for a privately-funded border fence on private land in Sunland Park, New Mexico. Cedar Attanasio / AP

"The construction of the wall at this point is, is in violation of city ordinance," said Sunland Park Mayor Javier Perea. The man who owns the property wasn't available for an interview, but his representative told CBS News that the government has long said to them there there is a natural barrier and that it doesn't make sense to put a wall there.

George Mason University law professor Ilya Somin believes the project may generate more publicity than impact.

"It's unlikely they're going to get the right to build more than a small section of wall on privately owned land, given that they can only do so if the owners want to let them," Somin said.

"What about the reality that you'll do it here and it may help this land owner, but in the larger scheme of things it'll sort of be a drop in the bucket," Begnaud asked Kolfage.

"Well, we aren't here to build an entire southern border wall," he said. "We're here to have an impact with the money that we raised to help these communities."