Homeland Security secretary touts border safety

And while the perception of security along the border has improved with increased Border Patrol presence, there are still some rural stretches where officials still complain of illegal crossings by drug smugglers and traffickers of illegal immigrants. "I would agree that it's better now than five years ago, but it still is a huge cat and mouse game with these guys," said Patrick Green, a sheriff's deputy in New Mexico's Hidalgo County.

Green talked about reports of vehicle and firearms thefts and break-ins in ranches along the borderland.

Napolitano said that while the Border Patrol launched large scale operations in sectors like San Diego, Tucson, El Paso and the Rio Grande Valley in south Texas, there are still sparsely populated rural areas where they are increasing the presence of agents, deployed sensors and installed or outposts. "That's not to say there will never be an illegal crossing on the Southwest border. ... People with common sense understand that."

The Border Patrol made 356,873 apprehensions on the Mexican border during the 2012 fiscal year, up 8.9 percent from the previous year but still hovering near 40-year-lows. U.S. Customs and Border Protection's budget nearly doubled to $11.7 billion in 2012 from $6.3 billion in 2005, according to figures from the Migration Policy Institute.