Just one month after Homeland Security Janet Napolitano announced the cancellation of a troubled virtual fence project along the southwest border, a new government report says that less than half of the 2,000 miles separating the U.S. and Mexico is "operationally controlled" by the Border Patrol.

The Government Accountability Office report, released this week, found that only 129 miles are under "full control" of the Border Patrol, leaving the rest "vulnerable to cross-border illegal activity."

The study examined the Border Patrol's ability to detect and respond not only to illegal activity on the immediate border but also after entry into the U.S.

The report found that 873 miles are under "operational control," which is only 44 percent of the entire Southern border. But the report said the 837 miles is on average an increase of 126 miles each year since 2005.

Republicans have seized on the report, saying it contradicts Napolitano's recent remarks that the administration's "border security approach is working."

"It is outrageous that DHS officials would make claims that the border is secure when according to the nonpartisan Government Accountability Office, the Border Patrol has 'operational control' over less than half of the Southwest border," Texas Rep. Lamar Smith, the chairman of the House Judiciary Committee, said in a statement.

"Forty-four percent is a failing grade," he said. "Administration officials are either blissfully unaware of the massive holes in security along the Southern border or are intentionally misleading the American people. Neither is acceptable."

The department has vigorously defended its efforts on the border ever since Napolitano canceled the SBInet, a project that aimed to implement a system of cameras and sensors which would allow officers to monitor crossings and dispatch Border Patrol agents to catch anyone entering the U.S. illegally.

The department is now pursuing a "new path forward" for security along the border that includes different technologies in different areas, Napolitano has said.

The department has noted that the administration has doubled the number of agents since 2004 to more than 20,500 and that the deployment last year of 1,200 National Guard troops and other initiatives have helped border officials seize more cash, more illegal drugs and more illegal weapons over the past two years.

But Napolitano said this week that the numbers need to improve faster in the Tucson sector, one of the most highly trafficked areas of Arizona.

The GAO report comes on the same week that a drug cartel in Mexico killed a federal agent and wounded another, prompting calls from Republicans for increased security measures.

In President Obama's budget for next fiscal year, which was released this week, he requests $43.2 billion for homeland security, an increase of $300 million from last year. The Republican-controlled House just passed a spending bill that gives $41.5 billion to the department, a 3 percent decrease from 2010.

Napolitano told the Senate Homeland Security Committee this week that the president's request would enable the department to secure the border.

"At the border itself, you need manpower, you need technology, you need infrastructure," she said. "Some of the things in the president's budget will really assist in this regard because they will allow us to complete some interoperability projects in terms of communications along the border."