"No one number captures the evolving and extensive nature of the border," Napolitano told the Senate Judiciary Committee during a hearing about the immigration bill. "There's no one metric that's your magic number."
Measuring the effectiveness of the $3.5-billion-a-year Border Patrol has long proved to be an elusive task. Several years ago, the agency rated its performance by assessing how much of the border was under "operational control." Officials determined "control" by measuring the agency's ability to detect, respond to and interdict migrants crossing the border.
By 2010, the agency reported that 44% of the border was under operational control, including about 85% of the section in California. Border Patrol officials focused on the improvement over past years, arguing that the figure showed a steady increase in effectiveness. Critics pounced on the agency's tacit admission that 56% of the border was not under control and said the agency was underperforming.
The agency has since discontinued the use of operational control as its yardstick and now cites migrant arrest totals as a measure of performance. Homeland Security officials, pointing to declining arrest numbers in recent years, repeatedly have said that the border is more secure than ever.
But a 2012 report by the Government Accountability Office, the investigative arm of Congress, said the use of arrest totals did not measure actual results and could lead to reduced oversight and accountability of the agency. Other experts have noted that the poor economy in the U.S. in recent years has discouraged workers from coming across the border. As the economy improves, no one knows whether that trend will quickly turn around.
One consistent problem is that border agents lack a reliable way of counting the number of people they don't see. To remedy that, senators have pointed to a new radar system developed to detect insurgents planting bombs in Afghanistan as one piece of technology that could help track people crossing unlawfully into the United States.
Called Vader, the drone-mounted radar has been tested over a 150-square-mile patch of Arizona desert for more than a year.
Homeland Security officials are also developing a new set of measurements called the "border condition index." Officials say the index will track trends in apprehensions, including the percentage of criminals stopped, where migrants are coming from and whether people are trying to cross again and again.
But the officials have emphasized that the purpose of the new index is to help them decide where to send more agents, not to give an overall score for border security.
Members of Congress have reacted with incredulity to claims that the department cannot come up with a single figure to measure border security.
"Excuse me," Rep. Candice S. Miller (R-Mich.) said at a recent hearing of the House border security panel that she chairs. "I'm just trying to let this all digest here." Without "a high degree of confidence that we are securing our border," she said, "I think this whole comprehensive immigration reform is going to be a very difficult lift."
Marosi reported from San Diego and Bennett from Washington.