President Bush will use a prime time speech Monday night to call for thousands of National Guard troops to be deployed along the Mexican border to help back up the U.S. Border Patrol.

The president will follow it up by visiting the U.S.-Mexico border in Yuma, Ariz., on Thursday, White House spokesman Tony Snow told reporters on Monday.

Snow said Bush's National Guard proposal would use "a very small percentage of the Guard." Out of about 400,000 National Guard members, the president is expected to call for fewer than 10,000 to help secure the border on a temporary basis. Those Guardsmen are not expected to carry out law enforcement duties, however, but would play a supportive role to Border Patrol agents.

Watch President Bush's primetime address Monday night at 8 p.m. EDT on FOX News Channel.

"I believe in strong border security," Senate Minority Leader Harry Reid of Nevada said on the Senate floor Monday afternoon. Reid said if the National Guard can be logically placed on the border and the money can be found to finance it, "I'll go along with that."

Bush's Monday night remarks come as the Senate tries to pass a guest worker proposal that opponents say doesn't do enough to stem the influx of illegals passing over the southern border each day. Senators began debate Monday on an immigration reform package that aims to allow the estimated 11 million to 12 million illegals in the United States look for a way to stay here.

Senate Judiciary Committee Chairman Arlen Specter, R-Pa., who's managing the immigration reform bill on the floor, announced Monday that party leaders have agreed to allow 30 amendments to be offered on the bill. Senate Majority Leader Bill Frist, R-Tenn, has said those votes will run on a "rigorously enforced" 15-minute vote schedule, Specter announced.

Frist is set on getting a final vote on the Senate bill by the middle of next week, Specter said.

The president supports a guest worker plan, but also must answer to many in his base who say border security is step one in dealing with the flood of illegal immigrants .

The conservative think tank, the Heritage Foundation, released a report Monday that said if enacted, the Comprehensive Immigration Reform Act would allow "an estimated 103 million persons to legally immigrate to the U.S. over the next 20 years -- fully one-third of the current population of the United States."

Separately, U.S. Sen. Jeff Sessions, R-Ala., unveiled an impact analysis that shows the Senate immigration bill "would permit up to 217.1 million new legal immigrants into the United States over the next 20 years, a number equal to 66 percent of the total current population of the United States."

Aside from the pressure at home, Bush is being forced to walk a diplomatic tightrope with Mexican President Vicente Fox, who called the U.S. president on Sunday to discuss efforts to improve border security. Bush emphasized to Fox that any move to put military units at the southern U.S. border was not an intimidation tactic aimed at his government, White House spokeswoman Maria Tamburri told FOX News.

"Mexican President Vicente Fox reached out to President Bush this morning to relay his concerns about consideration of a plan by the United States to deploy National Guard forces to the border region. President Bush made clear that the United States considers Mexico a friend and that what is being considered is not a militarization of the border, but support of Border Patrol capabilities, on a temporary basis, by National Guard personnel," Tamburri said.

"The president reiterated to President Fox his commitment to comprehensive immigration reform," she added. Fox's office also released a statement saying Bush assured the Mexican president that any military support would be administrative and logistical and would come from the National Guard, not the Army.

The White House on Monday dismissed criticism that the National Guard troops would militarize the 2,000 mile line between the U.S. and Mexico.

"They will not have law enforcement powers in and of itself but they will help building infrastructure, surveillance, and those things, so it's not necessarily a militarization of the border, but what it is is filling an immediate need to free up more border patrol agents so they can do the arresting and detention there on the spot," Dan Bartlett, White House presidential counselor, told FOX News.

White House aides were working on the details of the president's proposal and how to address the concerns of critics, including Govs. Arnold Schwarzenegger of California and Bill Richardson of New Mexico, among others, who say using Guardsmen to man the border would further burden an overextended military. Domestically, governors traditionally are the ones with the authority to redeploy National Guard troops within their states.

"What in the world are we talking about here? Sending a National Guard (for whom) we may not have any capacity to send down to protect the borders? That's not their role," said Sen. Chuck Hagel, R-Neb., on ABC's "This Week."

"We have stretched these men and women so thin, so thin, because of the bad mistakes done by the civilians in the military here, that I wonder how they're going to be able to do it," added Sen. Joe Biden, D-Del.

Hagel said he helped write a bill under debate in the Senate that would double the 12,000-strong Border Patrol force over the next five years.

"That's the way to fix it, not further stretching the National Guard," he said.

'We've Got to Secure Our Borders'

On Sunday, the president's national security adviser, Stephen Hadley, said the "huge task" of safeguarding the border will be left to Border Patrol.

About 100 National Guard troops are serving on the border to assist with counter-drug operations, heavy equipment support and other functions.

"I think what it would be is simply expanding the kind of thing that has already been done in the past in order to provide a bit of a stopgap as the Border Patrol build up their capacity to deal with this challenge," Hadley told CBS' "Face the Nation."

But Rep. Charlie Norwood, R-Ga., a border security proponent and backer of the Minuteman groups shoring up the border with volunteer "spotters," wrote in an editorial Sunday in Human Events Online that Arizona Gov. Janet Napolitano already tried to redeploy 170 National Guardsmen on the troops and it didn't do much because the numbers were too small and their role was to help Border Patrol with cargo screening, not guarding the unprotected areas along the border.

Norwood said the truth in Bush's commitment to border security "will lie in the proposed numbers, and whether the plan is for a short-term demonstration project or a long-term strategy for truly securing our southern border."

He added that research data done by the House Immigration Reform Caucus shows that "the southern border can be virtually closed except at legal points of entry within a one-month period — at the longest. ... It will initially take 36,000 troops.

"At the start, they should be National Guard personnel drawn nationally. There isn't enough National Guard in the border states alone to do the job without hindering combat readiness, so the forces will need to be pulled from other states as well under current National Guard Bureau assistance regulations," Norwood said.

That's the position favored by the Minuteman Project, whose leader Jim Gilchrist told FOX News he thinks the president's proposal will just be a "head fake."

"Apparently, they just do not get the message and 5,000 National Guardsmen is not enough. You need 25,000 Guardsmen ... to supplement the Border Patrol until they can find another 25,000 agents and train them. That will take several years," Gilchrist said.

The Senate immigration reform measure is heavy on a guest worker plan, though Frist has repeatedly called for tightening the borders.

"We've got to secure our borders," Frist said on a cable news network on Sunday. "We hear it from the American people. We've got millions of people coming across that border. First and foremost, secure the border, whatever it takes. Everything else we've done has failed. We've got to face that. And so we need to bring in, I believe, the National Guard."

He added that any lawmakers who have doubts about the National Guard — well trained after years in Iraq and Gulf Coast duty following Hurricane Katrina last year — are "whining" and "moaning."

Bush on Monday night will deliver his speech from the Oval Office, where he is expected to stress protecting the border and accommodating many of the millions of illegal immigrants already in the United State.

He likely will argue that many of the illegal immigrants in the United States now should be allowed to pursue a path to citizenship that would include learning English and paying back taxes and fines, all elements of the Senate bill.

But the Senate bill is a long way from the House version of immigration reform passed last December. That measure does not address the guest worker issue but increases penalties for illegal immigration activities and funds a 700-mile border fence.

Former House Speaker Newt Gingrich said if Bush can push through an immigration reform bill that avoids amnesty but tightens the borders, it could go a long way toward improving the president's sagging poll numbers.

"I think that the president, by doing the things that resonate with the American people, could rebound very quickly. I've seen presidents come back dramatically when people say they go the message, now they're doing the things I want," Gingrich told FOX News.

FOX News' Megyn Kendall, Julie Kirtz and Sharon Kehnemui Liss and The Associated Press contributed to this report.