A senior US Republican is pushing for the construction of a 2,000-mile (3,200km) fence along the entire length of the US-Mexico border.
The US is happy to see managed, legal migration and border travel
Duncan Hunter, who chairs the Armed Services Committee in the House of Representatives, hopes to win enough support to pass a bill in Congress.
Critics of his bill say many immigrants enter the US legally but simply remain in the country when their visas expire.
More than 1m Mexicans are stopped from entering the US each year to seek work.
Mr Hunter's plan for the fence envisages a dual-layer construction equipped with electric sensors stretching from the Pacific Ocean across to the Gulf of Mexico.
The fence would be surrounded by a new border buffer zone to the north and would be studded with 25 new official points of entry along its route.
A 14-mile (22km) westerly stretch of the border to the south of San Diego is currently protected by two layers of fencing.
Much of the lengthy frontier, though, is barely patrolled and protected only by ditches or barbed wire at best.
"Illegal aliens continue to funnel directly into many of our local communities and adversely impact our way of life," said Mr Hunter, a California congressman.
He said that the lessons of 11 September 2001 taught Americans that immigration was a national issue that required national solutions.
Earlier this week Homeland Security Secretary Michael Chertoff said he aimed to achieve an "extremely high probability of detecting, responding to and interdicting" all illegal immigration.
In the absence of a fence, independent groups such as the Minutemen have begun patrolling stretches of the border hoping to catch illegal migrants.
Opponents of the fence have criticised its likely costs - estimated at about $8 billion (£4.5bn) - and the slim chances of wiping out all illegal immigration.