Rep. Bennie Thompson, D-Miss., told reporters this week that he expected to "re-visit" the issue when he becomes chairman of the House Homeland Security Committee in the 110th Congress, which has a Democratic Party majority.
He said that the high technology Secure Border Initiative, or SBI Net -- essentially a set of monitors, cameras and other integrated surveillance systems to monitor the border -- was a viable alternative.
"We might do away with it, or look at (integrating it into) SBI Net," he said, "A virtual fence rather than a real one."
The Secure Fence Act, one of the laws passed by the GOP-controlled Congress in a pre-election flurry of border security legislation, mandates 700 miles of fencing in five sections, and defines where on the 1,951-mile southern border they should go.
As a result, some administration officials view it as an example of congressional micro-management, and might welcome changes that gave them more flexibility.
Department of Homeland Security Spokesman Russ Knocke told United Press International that in remote border areas, "virtual fencing ... is more advantageous," whereas "traditional fencing has a core role in our border security strategy ... especially in urban areas."
"We're optimistic that working with Congress we'll get the flexibility to integrate traditional fencing into a seamless, high-tech border security system," Knocke said.
Notable deaths of 2014 [PHOTOS]