Back in 1994, Barbara Boxer wanted to put National Guard troops on the border. From an August 1994 L.A. Times article:

Ten months after Sen. Barbara Boxer secured federal funds to deploy National Guard troops to hinder illegal immigration, the program has not been implemented anywhere in the country and the Department of Defense has no plans to do so.

Last year, the first-term California senator hailed her so-called "Boxer National Guard Plan" as an innovative solution to the state's illegal immigration problem. Supplementing federal Border Patrol agents with "well-trained, well-equipped" military personnel, Boxer said at the time, "could prove the most cost-effective way to bolster enforcement at the California border."

Soon after Congress passed the legislation, however, the Defense Department ruled that the plan lacked any legal authority and decided not to carry it out...

...Like many politicians in California, Boxer succeeded in attracting favorable attention for her efforts to crack down on the tide of immigrants who enter the country illegally. The senator's staff pointed to a Times poll last fall that found that 73% of Californians supported using the National Guard to halt illegal border crossings...

...The prospect of armed forces in military uniforms assisting in immigration patrols at the nation's borders for the first time in history drew protests from civil rights groups and criticism even from Republican hard-liners on the issue such as Gov. Pete Wilson. He called the plan "not helpful" and a violation of an international treaty that bans armed troops on the border.