EL CALABOZ, Texas (CNN)  -- Eloisa Tamez said she isn't scared anymore, just determined. "I am not backing down," she said.

The U.S. government wants to build a border fence like this one. About 100 landowners are fighting it.

Tamez owns three acres of land along the Texas-Mexico border where the Department of Homeland Security would like to build a border fence. The property is a remnant of a 12,000-acre grant from Spain to her family in 1767, before the United States even existed.

"It is my history. It is my heritage," Tamez said.

This week, the Justice Department began legal action against landowners and municipalities who have refused to give government surveyors access to their land.

Tamez expects she will be sued sometime soon, but she is not intimidated.

Asked how long she will fight, she said, "As long as I have to."

Michael Chertoff, the Secretary of Homeland Security, said the fence will not be stopped by opponents like Tamez.

"Can we simply abandon an enterprise because it is a problem for a particular individual?" Chertoff told CNN. "I don't think I can accept that."  Watch Chertoff say it's "civic responsibility" to give up land »

Chertoff believes a fence would curb the steady stream of illegal immigrants making their way across the border and lessen the flow of drugs. He also argues it will increase the safety of Border Patrol agents who have faced increasing violence.

The government wants to build 700 miles of fence along the Mexican border, including 370 miles of it by the end of this year. About 70 miles of fence is to be built in the Rio Grande Valley by year's end, if the government gets its way.

The Rio Grande forms a natural barrier along this stretch of the border, but in some places it is narrow enough to swim across.

On the banks of the river there is ample evidence that people do so. Piles of underwear lie discarded by swimmers after they make it across. The swimmers change into dry clothes they have carried across in plastic bags. Then they disappear into the United States.

The Border Patrol has stepped up its efforts in the Rio Grande Valley with more lights, and sensors to pick up movement. A levee built along the river has a muddy road on top used by Border Patrol vehicles to patrol the area.

Richard Cortez, the mayor of the border town of McAllen, Texas, believes hiring more Border Patrol agents, deepening the Rio Grande, and clearing its banks of tall vegetation would provide better border protection than the fence.

Cortez calls the fence "a multibillion-dollar speed bump," which will slow, but not stop, illegal immigration.

"It is a false sense of security," he said. "America will not be safe. America will continue to waste resources on something that is not going to work."

Cortez and other border mayors who oppose construction of the fence formed a group called the Texas Border Coalition. The coalition wrote to Chertoff asking for further consultations on the fence, but this week the Department of Homeland Security turned them down.

While expressing support for open dialogue with residents and officials, David Pagan of U.S. Customs and Border Protection wrote in an e-mail, "We do not plan to suspend work on the construction of fence in order to hold a series of additional consultation meetings."

Cortez said his city is contemplating a court test of the law that mandated the construction of the border fence.

And so a battle is being waged by about 100 landowners, those like Eloisa Tamez who are standing firm.   "I will not allow them to come and survey my land. I have an American-given right to protect my property," she said. E-mail to a friend
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question: What does the Mayor call the fence?, answer: "a multibillion-dollar speed bump," | question: What does the government want the land for?, answer: to build a border fence. | question: Who want land for border fence ?, answer: The U.S. government | question: Whose property has been in their family for many decades?, answer: Eloisa Tamez | question: Who said that he won't relent "for a particular individual"?, answer: Michael Chertoff, | question: Who wants to buy the land?, answer: U.S. government | question: What did the border town mayor call the fence?, answer: "a multibillion-dollar speed bump," | question: what year is mentioned, answer: 1767, | question: what does the mayor think of the fence, answer: "a multibillion-dollar speed bump," which will slow, but not stop, illegal immigration. | question: Who said that their  property has been in their family since 1767 ?, answer: Eloisa Tamez | question: Who refuses Government bid for land for fences?, answer: about 100 landowners, those like Eloisa Tamez