More than 500,000 foreign visitors who came to the United States last year failed to return before their visas expired, according to a new report by the Department of Homeland Security.

Jessica Vaughan, director of police studies at the Center for Immigration Studies, noted on “The Laura Ingraham Show” on Wednesday that more than 12,000 of those people came from countries associated with terrorism.

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“It is a huge number,” she said. “It’s bigger than people expected.”

The numbers were included in the annual Entry/Exit Overstay Report. The overstays include only people who came as tourists or on business trips. It does not include that vast number of people who come on other nonimmigrant visas, such as temporary workers or millions of visa waiver recipients.

Sen. Jeff Sessions, an Alabama Republican who chairs a subcommittee with jurisdiction over immigration, is holding a hearing Wednesday afternoon exploring why the Obama administration has not yet implemented a biometric exit tracking system required under the law. Sessions indicated he also plans to probe the administration’s enforcement record.

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Vaughan called the overstays a “huge problem” that accounts for about half the population of illegal aliens living in the United States. She said it is a security risk as well. The problem, she said, arises from a combination of factors.

“This is partially an outgrowth of the huge increase — about 25 percent in issuance of nonimmigrant visa that the Obama administration has brought about,” she said. “But it also reflects the fact that there is very little enforcement of our immigration laws. And, you know, the president is giving overstayers a free pass.”

The government report says 416,500 of the 527,127 visitors who failed to return home on time were still in the United States as of Jan. 4. Those people, Vaughan said, have joined the population of illegal immigrants.

About 29 percent of the visitors who failed to go home gained entry under a program that gives citizens from 38 pre-approved countries the ability to come to America without a visa. Congress late last year tightened restrictions, giving the Department of Homeland Security the authority to suspend the waivers to travelers whose countries fail to share intelligence about terrorism. But lawmakers this month sponsored a bill to undo some of those reforms after complaints from the tourism industry.

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Vaughan noted that the Gang of Eight immigration overhaul that passed the Senate in 2013 but died in the House would have expanded the visa-waiver program to about half of the world’s countries. That includes China, Saudi Arabia, Russia, India and Mexico. Ingraham noted Republican candidates have pledged to deal with the program.

“I wonder how they’re going to deal with it,” she said. “Are they just going to waive them in and say this is not a problem? Or, you know, the way it should be dealt with — which is to enforce the law and to stop issuing so many visas. That’s the way to bring the illegal population down.”

Vaughan said visible enforcement likely would lead to greater compliance.

“A lot of these people, I think, would comply with the visas if there were any threat at all that they might be removed to their home country,” she said. “But there is no deterrence, because there is no enforcement, and the president broadcasts that there’s no enforcement.”