While the Senate immigration bill devotes hundreds of pages to immigrants who enter the U.S. illegally over the Southwest border, it pays little attention to another but equally persistent problem: those who enter legally but never leave. In Washington and in the immigration business they're known as visa overstays.

An estimated 40 percent of the 11 million to 20 million undocumented immigrants in the U.S. came here legally, but stayed after their visa expired. Yet, the Obama administration has made little or no attempt to track or deport visa overstays.

"Clearly it's a flaw, that is a problem," said Brian Jenkins, an adviser to the Rand Corp. and a terrorism expert. "And we do have a handful of cases among those who have been arrested in terrorist plots who were here overstaying a visa."

In 2007, Hosam Smadi arrived from Jordan on a 90-day tourist visa but never left. Two years later he plotted to blow up a Dallas high-rise with a car bomb.

Another tourist, 29-year-old Moroccan Amine El Khalifi, overstayed his visa and last year conspired to detonate a bomb at the U.S. Capitol.

Rep. Candice Miller, a Michigan Republican on the House Homeland Security Committee, calls visa overstays a national security issue. 

"We all remember 9/11," Miller told Fox News. "Four of those murderers, cowards, terrorists were visa overstays. They came on student visas and never left. So it is a very important component to our border security and national security."

On multiple occasions, first after the 1993 World Trade Center bombing, and again after 9/11, Congress mandated that immigration officials come up with a verifiable entry-exit system to track foreign visitors. To date, the Department of Homeland Security has failed, despite spending billions in tax dollars.

The current system, known as USVISIT, does take fingerprints and photos of international visitors when they arrive at U.S. airports, but it has no similar biometric exit system. The goal is to match entry and exit records to determine which individuals comply with their visa and sanction or deport those who do not.

However, airlines and the tourism industry have fought against the congressional mandate. They oppose any additional costs, responsibilities or procedures that might reduce foreign travel to the U.S.

Originally, the U.S. envisioned a biometric based system -- where foreign tourists, students and businessmen would provide 10 fingerprints and an eye scan when they enter and exit the country. However, it proved expensive and time consuming. So currently the U.S. only does this when visitors enter at the airport. There is no exit control whatsoever, so officials have no idea who overstayed their visa.

Former 9/11 Commission member and Senate Judiciary staffer Janice Kephart says lawmakers and the Obama administration are making a mistake if they overlook overstays. 

"Exit means you have a tracking system for people, a tracking system for people means that ICE (Immigration and Customs Enforcement) now has data to enforce the law against overstays. We don't have that," she says.

But one country does – Australia. Tourists traveling there have their passports scanned when they enter and when they leave, as well.

The proposed U.S. Senate bill envisions a similar entry-exit system at airports and seaports within five years. The proposal doesn’t address the ports of entry on the Mexican border.  Backers of the bill say it is not ideal, but better than what the country has now.

"I say slap another fee on the visa," says Miller. "It's a privilege to come to the U.S. Let’s make sure we have the resources we need to track people when they arrive and when they leave."

The Senate bill is scheduled for a full hearing in the Judiciary Committee on May 9.

William La Jeunesse joined FOX News Channel (FNC) in March 1998 and currently serves as a Los Angeles-based correspondent.