If the deployment reaches 15,000 troops, it would be roughly equivalent to the size of the US military's presence in Afghanistan and three times the size of the presence in Iraq.
Already, the deployment is believed to be the largest of its kind in more than a century.
The decision to deploy such a large number of troops in the days before the Midterm elections has resulted in accusations from critics of the President that he is using the issue as a political stunt designed to fire up a base concerned about immigration.
Defence Secretary Jim Mattis, speaking to reporters during a visit by the South Korean defence minister to the Pentagon, rejected the criticism, saying that the military was deploying to support the Department of Homeland Security and Customs and Border Protection.
"The support that we provide to the Secretary for Homeland Security is practical support based on the request from the commissioner of customs and border police, so we don't do stunts in this department," Mattis said.
The Defence Secretary said the military had carried out similar missions within the United States following natural disasters. "We are there in support of the Secretary of Homeland Security, who needs additional military assistance," he said.