Visa enforcement is in the Gang of 8 plan. The US-VISIT law passed in 1996 was supposed to solve the visa overstay problem. It is why we have machine readable visas. The problem is enforcement, not the lack of laws.
At this point, the House is right to just say "eff it, Obama can't be trusted to enforce anything." Paul's certification plan was an attempt to address this but with Obama being so lawless it's almost pointless.
But it's also true that the law needs to be changed so stop issuing so many Visas to hostile nations in the first place.
Visa Enforcement : I believe our greatest national security threat is our lack of security at the border. On 9/11, 16 of 19 hijackers were here on "legal" student Visas but were not in school or in the states they were supposed to be in. Ten years later we are still not policing who we grant Visas to. We gave a Visa to a Nigerian who had made two trips to Yemen, bought a one way ticket with cash and no baggage and his dad tipped off the US Embassy that he had been radicalized. I propose a moratorium on Visas from about ten rogue nations or anybody that has traveled to those nations. I would keep this in place until our government proves they can manage intelligently our Visa process. Source: www.randpaul2010.com/issues (12/29/2010)