With his rivals embracing aggressive stands against illegal immigration, New Jersey Gov. Chris Christie said that if he is elected president, the United States would track foreign visitors just like FedEx tracks packages.

"At any moment, FedEx can tell you where that package is. It’s on the truck. It’s at the station. It’s on the airplane," Christie said while campaigning in Laconia, N.H. "Yet we let people come to this country with visas, and the minute they come in, we lose track of them.

"So here’s what I’m going to do as president: I’m going to ask Fred Smith, the founder of FedEx, to come work for the government for three months, just come for three months to Immigration and Customs Enforcement and show these people."

The remark elicited laughter and some clapping from the crowd, but it shows again how serious the Republican field of presidential contenders is about catching up to billionaire Donald Trump, whose campaign has been built in part on such tough talk.

Trump repeatedly has called for building a massive impenetrable wall along the border to prevent illegal border crossings. But Christie indicated that about 40 percent of the illegal immigrants likely wouldn't be affected by such a wall —because they are allowed in legally with a visa, and then overstay their visit.

"We need to have a system that tracks you from the moment you come in," Christie said, just like FedEx, to monitor those people who come in with visas. "Then when your time is up … then we go get you, tap you on the shoulder and say  ‘Excuse me, thanks for coming,  time to go.' That would cut 40 percent of the problem we’ve developed over the last 30 years."

Fred Smith's daughter, Samantha Smith, was reportedly hired as the Christie campaign's communications director earlier this year.

The details of how a Christie administration might track human beings in the same way that FedEx tracks deliveries have not been announced. FedEx declined to comment.

Already, some Twitter users have sarcastically remarked that the candidate might want to mark each immigrant with indelible symbols for easier electronic scanning.

"I got relatives with numbers printed on their hands, so why not just barcode these Mexicans?" one user said.

For decades, critics have noted that the United States has had massive troubles monitoring foreign visitors who enter the country with legal visas but then overstay their allotted time.

Exactly what percentage of undocumented U.S. residents arrived with visas has been a subject of varying estimates, but Christie's estimate of 40 percent generally resembles the estimates that have been offered by researchers at the Pew Hispanic Center and the Department of Homeland Security.

In 2006, the Pew Hispanic Center estimated that 40 to 50 percent of unauthorized residents entered the country legally, most coming as tourist or business visitors. An earlier estimate from Department of Homeland Security estimated that one third of illegal immigrants in the United States were people who had overstayed visas.

His remarks in New Hampshire also underscore just how far Christie has changed his stance on immigration. In 2010, in his first months as governor, he favored securing the border as well as "a common sense path to citizenship for people." But earlier this year, Christie said he no longer supported the path to citizenship for undocumented residents and, in fact, criticized Democratic presidential candidate Hillary Rodham Clinton's plan as "pandering."

Other Republican candidates have changed their positions on immigration, too, apparently believing that Trump has "touched a nerve" with his vision for an enormous border wall.

Polling, however, indicates that Americans generally have mixed opinions about immigration issues.

In July, a Washington Post-ABC News poll showed that 60 percent believed that undocumented immigrants should be allowed to become citizens or permanent residents if they pay a fine and meet other requirements. About 57 percent said that immigrants from other countries "mainly strengthen" American society.

By engaging in the tough talk to win Republican voters, some political analysts say, the candidates may be undermining their chances in the general election.