(CBS/AP) The number of Mexican migrants trying to sneak into the United States through the Arizona border has dropped by half since hundreds of American civilians began guarding the area earlier this week, say Mexican officials assigned to protect their citizens.

But that doesn't mean the migrants have given up. Most remain determined to enter the United States and say they will simply find other places to cross.

Before Minuteman Project volunteers began patrolling, Mexican officials encountered at least 400 undocumented migrants daily. On Monday, the second day Minutemen were present, they spotted just 198, said Bertha de la Rosa of Grupo Beta, a Mexican government-sponsored group that discourages people from crossing illegally and aids those stranded in the desert.

"The fact that we're not seeing them here doesn't mean they are not trying to cross," said de la Rosa, the group's coordinator in Agua Prieta, a town across the border from Douglas, Ariz. "They say they will look for another place or wait awhile — but they are not giving up."

Grupo Beta, along with armed state police officers, began patrolling the Mexican side of the border on Sunday.

Jose Luis Mercado is among those determined to cross.

Mercado, a farm worker from central Mexico state, was one of 10 migrants who walked through the desert all night Monday and early Tuesday before they were abandoned by the smuggler they had paid to get them across the border.

"He just said it was too risky to cross and to wait for him, but he never came back," Mercado said.

Mercado, like most migrants trying to cross into the United States from this dusty border city, had been unaware of the Minuteman Project, despite extensive news media coverage of the group.

He and his companions were resting in a ditch littered with plastic bottles, clothes and empty tuna cans when they were spotted by Grupo Beta agent Hector Salazar.

"There are a lot of people trying to catch you," Salazar told the migrants as a small plane and then a U.S. border patrol helicopter flew over the barbed-wire fence dividing the border.

"It's not only border patrol, but also armed civilians," Salazar said. "Don't give them the pleasure of detaining you."

But the migrants declined Grupo Beta's offer for a discounted bus ticket back home. They vowed to attempt the crossing as many times as it took to make it into the United States.

"I'm going to risk it and try somewhere else," said Mercado, 40, who has five children and earns $60 a week. "I have no other option. I want to be able to pay for my children's education so they don't have to go through all this."

Pro-migrant activists say people unable to cross in Agua Prieta have begun arriving at shelters in Nogales, about 80 miles west, and in Altar, a town about 125 miles southwest.

Minutemen organizers initially promised as many as 800 volunteers would participate in the monthlong migrant-monitoring project at one time or another. They say about 480 have shown up thus far. There was no way to independently verify that number. Authorities were not keeping count.

The Minutemen, some of whom are armed, say their purpose is partly to draw attention to the high influx of migrants across the Arizona-Mexico boundary, considered the most porous stretch of the 2,000-mile U.S.-Mexico border. Of the 1.1 million illegal migrants caught by the U.S. Border Patrol last year, 51 percent crossed at the Arizona border.

But in Mexico and Central America, the volunteers are seen as "hunters of illegals" or racists.

"They have a right to patrol their border, but I only want to cross to find work," said Vidal Sanchez, a 26-year-old farmer who was walking through Sonora's scrub-covered desert Tuesday.

"If they detain us, I'm going to tell them I need to work. I think they'll understand."

A State Department official said the implementation of the law will be done in three phases, beginning the end of this year, reports CBS News' Charles Wolfson. The new rules, to be completed by Jan. 1, 2008, were called for in intelligence legislation approved last year by Congress.

Safeguarding U.S. borders are a top concern of U.S. intelligence and security officials. The concern increased after the Sept. 11, 2001, terror attacks on the World Trade Center in New York and on the Pentagon.

The travel industry has raised concerns that the changes might hamper tourism, one official said.

The announcement follows a three-way summit last month that President Bush held with Prime Minister Paul Martin of Canada and President Vicente Fox of Mexico.

Francisco Garcia, a volunteer for Altar's lone shelter, said most migrants dismiss the Minutemen as "crazy people" — but for migrants' rights activists, the situation is worrisome.

"For us, it's clear to see things could get out of control because those in the migration business are not easily intimidated," Garcia said. "We're afraid an aggression could escalate into an international incident."

© MMV, CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.

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