At a stop to inspect border security in El Paso on Tuesday, Napolitano said the argument ignores gains made in illegal immigrant captures as well as seizures of drugs, weapons and currency.
She also said the argument's fundamental flaw is contending that border security is unrelated to interior enforcement such as verification of legal residence of job applicants.
Napolitano said the immigration "system as a whole is badly in need of reform." It is, she said, inextricably linked with interior enforcement, visa reform and the process for legal migration, a pathway to citizenship and earned pathway for those already here.
A bipartisan group of senators wants assurances on border security as Congress considers proposals that would bring the biggest changes to immigration law in nearly three decades. Last week, the group of senators released a blueprint that would bring a path to citizenship for people living in the U.S. illegally, but they demanded assurances on border security first.
President Barack Obama does not endorse such a linkage in his own immigration proposal. But Republicans in the Senate group, including John McCain of Arizona and Marco Rubio of Florida, say they cannot support an immigration bill that doesn't make a pathway to citizenship conditional on a secure border.
"I believe the border is secure. I believe the border's a safe border.
The current administration has "deployed historic levels of personnel, technology and infrastructure to help secure the Southwest border," she said Tuesday. It has meant that attempts to illegally cross from Mexico are half of what they were in 2008 and a 78 percent down from their peak in 2000. "The numbers are the numbers," she said.
Last year only, the El Paso sector saw an increase of 71 percent in seizures of currency, 39 percent more drugs interdicted and a 139 percent of illegal weapons seized, the secretary said. The sector includes far West Texas and all of New Mexico.
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.