Brewer, who in 2010 signed a controversial immigration law that allows law enforcement to check the documentation of suspects they think immigrated illegally, explained that the border in her home state is currently not secure.

"We need more fencing — secure fencing; we need more electronic equipment, drones, surveillance cameras," Brewer said. "I think we need more boots on the ground. I think they should be closer to the border and away from the border."

Lawmakers debated the so-called "Gang of Eight" immigration reform bill at a Senate Judiciary Committee hearing on Monday.

The legislation gives a provisional legal status to more than 11 million immigrants currently living in the country illegally but only after a series of steps are taken to secure the border between the United States and Mexico. The criteria for a "secure border" under the bill include a 90 percent success rate for stopping illegal border crossings in high-risk locations. Those areas would also have improved surveillance under the bill.

Like Brewer, Sen. Jeff SessionsJeff SessionsICE chief faces rowdy crowd at Calif. forum Letters: Why is FDA favoring real cigarettes over fake ones? Overnight Cybersecurity: First GOP lawmaker calls for Nunes to recuse himself | DHS misses cyber strategy deadline | Dems push for fix to cellphone security flaw MORE (R-Ala.) has argued that the immigration bill proposal does not do enough to improve border security. 

In a recent interview on conservative host Hugh Hewitt's radio show, Sessions said the bill "only requires that [Secretary of Homeland Security Janet Napolitano] to, within six months — now this is after everybody’s been legalized, after, in effect, the amnesty has commenced — that she would submit a report on fencing, and a fencing plan."