President Bush, trying to build momentum for an overhaul of the nation's immigration laws, is considering plans to shore up the Mexican border with National Guard troops paid for by the federal government, according to senior administration officials.

One defense official said military leaders believe the number of troops required could range from 3,500 to 10,000, depending on the final plan. Another administration official cautioned that the 10,000 figure was too high.

The officials insisted on anonymity since no decision has been announced.

The president was expected to reveal his plans in an address Monday at 8 p.m. EDT. It will be the first time he has used the Oval Office for a domestic policy speech — a gesture intended to underscore the importance he places on the divisive immigration issue.

Watch FOX News Channel Monday night for full coverage of Bush's address.

The key questions Friday were exactly how many National Guard troops might be deployed, for how long and at what cost to taxpayers — as well as the problem of possible disruption of upcoming deployments to Iraq and elsewhere overseas.

Using those troops for border security is "maybe not the right way to go," said California Gov. Arnold Schwarzenegger, the Republican former movie star, though he agreed the federal government is obliged to secure the borders.

"Not to use our National Guard, soldiers that are coming back from Iraq, for instance, and they have spent a year and a half over there and now they're coming back," he said. "I think that we should let them go to work, back to work again."

Texas Democratic Reps. Silvestre Reyes and Solomon Ortiz — both senior members of the Armed Services Committee — sent a letter to Bush urging him to consider a number of issues before deploying the troops, including whether another mission is in the best interest of "our over-stretched military."

As discussions among the White House, the Pentagon and the states continued on how the military could be used to secure the southern border, defense officials said states want the federal government to pick up what will be a significant tab for the increased security. Officials had no estimates on that cost.

Bush's speech Monday night is intended to build support for broad immigration overhaul by taking substantive steps to secure the border.

"We need to beef up those (border) operations and the cost will be substantial," Sen. John Cornyn, R-Texas, said in an interview. "People are just not going to accept comprehensive immigration reform unless they are assured the government is going to secure the border. People have lost confidence in the federal government because they simply haven't addressed this in a dramatic and effective way."

Paul McHale, assistant secretary of defense for homeland defense, asked officials earlier this week to offer options for the use of military resources and troops — particularly the National Guard — along the border with Mexico, according to defense officials familiar with the discussions.

Cornyn said state officials are also looking for more unmanned aircraft, ground sensors, surveillance cameras and military training to help with border patrols.

Defense officials said the National Guard may be used only until significant additions to the existing civilian border patrols can be fully funded and completed.

Currently there are about 100 National Guard troops involved in counter-drug operations, including some along the border, said Guard Bureau spokesman Jack Harrison. He said there are also between 10-15 Guard members — mostly engineers — helping border patrol agents with vehicle and heavy equipment support.

The discussions this week underscored the importance of the border and immigrations issues, yet were tentative enough to reflect worries about drawing the nation's armed forces into a politically sensitive domestic role.

Southern lawmakers met with White House strategist Karl Rove earlier in the week for a discussion that included making greater use of National Guard troops to shore up border control. And on Capitol Hill, the Senate is poised to pass legislation this month that would call for additional border security, a new guest worker program and provisions opening the way to eventual citizenship for many of the estimated 11 million to 12 million illegal immigrants in the country.

Currently, the military plays a very limited role along the borders, but some active duty forces have been used in the past to help battle drug traffickers.

The National Guard is generally under the control of the state governors, but Guard units can be federalized by the president, such as those sent to the wars in Afghanistan and Iraq. Active duty military may not be used for law enforcement unless the president authorizes it.

In addition, under federal law, in certain circumstances the states can maintain control of their Guard units but arrange to have the costs picked up by the federal government. That allows the Guard to continue to perform law enforcement activities.

Officials wrangled over the use of the active military during Hurricane Katrina, with some suggesting that troops be used for law enforcement to quell violence and looters in New Orleans. There were also suggestions that Bush federalize the National Guard there, but state officials opposed that proposal. In the end, neither move was made.