Speaking at the U.S.-Mexico Congressional Border Issues Conference, Cornyn said he does not believe that the Obama administration has an adequate strategy for stopping illegal activity along the border.
"First, a good strategy would have an interagency approach," Cornyn said. "We already know that there are dozens of task forces across the Southwest border, and many of them are doing good work. But they are not yet coordinating our intelligence and interdiction operations as well as we should."
He said a "good model" for the administration to replicate along the border would be the Joint Interagency Task Force South in Key West, Fla. The task force is made up of officials from multiple agencies that target illicit trafficking in the waters of the Atlantic.
"This is designed to resolve the conflicts between different U.S. government agencies and make sure we know who's in the lead and what the chain of command is," Cornyn said. "This chain of command is important for coordinating the drug interdiction efforts in the Caribbean and South America."
"And many federal agencies, as well as representatives of sovereign nations, including Mexico, are part of it," he added. "This model has already drawn the attention of the Department of Homeland Security, but we have not yet seen that idea bear fruit."
Homeland Security Secretary Janet Napolitano, who spoke separately at the event, touted the administration's efforts to beef up security along the border with Mexico.
According to her, the administration has increased the number of Border Patrol agents to about 21,000; doubled the number of personnel assigned to Border Enforcement Security Task Forces; and deployed about one-quarter of all Immigration and Customs Enforcement agents to the Southwest border region-which Napolitano said is the most ever.
She added that the U.S. and Mexican governments have an unprecedented collaboration when it comes to law-enforcement cooperation, intelligence-sharing, and joint operations.
"We are not here to run a victory lap. We are here to tell you where we've been and where we are going," Napolitano said.
"This administration believes that security and economic prosperity are complementary. That's why we will continue to take actions on both fronts," she added.
Regardless, Cornyn, who has been a chief critic in Congress of the administration's handling of border security, cited a recent Government Accountability Office report that 1,120 miles of the U.S.-Mexico border are not under operational control.
"A good strategy should be resourced appropriately," Cornyn said. "My friend Secretary Napolitano talks about the resources that have been devoted -- the so-called inputs. Where I'm really more interested in what the results, or the outputs, are."
He added: "We're still not doing enough, in my view, to support local law enforcement that's had to bear the brunt of the federal government's failure to do its job along the border."
Cornyn said that the congressional stalemate over approving comprehensive legislation to overhaul the nation's immigration laws will continue unless more is done with regard to border security.
"Until the federal government does its job and regains the confidence of the American people that it will actually deliver a product as advertised … I think we're going to be where we are now, which is with no real opportunity in sight," he said.