Leading Texas Republicans fear the president's decision to delay the deportation of some longtime illegal residents will spark a new surge of border crossings if the message is distorted into a promise that the United States will grant free entry for all.

President Barack Obama's executive action last week applies to an estimated 5 million illegal immigrants whose children are U.S. citizens or legal residents. They will be eligible for work permits and receive a reprieve from deportation as long as they have lived in the United States more than five years and have no serious criminal record. But Texas Attorney General Greg Abbott insisted the policy nuances will not be clear to everyone contemplating an illegal border crossing.

"The people coming from Central America are typically not legal scholars who look into the depths of what the president is saying," Gov.-elect Abbott said during an appearance on "Fox News Sunday."

"All they hear is amnesty," agreed Alejandro Garcia, spokesman for Lt. Gov.-elect Dan Patrick.

A leader of a border agent union said Sunday he believes the surge has already started.

"We just caught two from Guatemala that had just crossed near the river," said Chris Cabrera, vice president of a McAllen chapter of the National Border Control Council. "They told us that they'd been here five years. They're already trying to take advantage about what they've heard."

Agents expect those crossing illegally to start saying the "magic words" to stop their immediate deportation, he said.

Human rights activists contend the speculation about a new surge of immigrants is the same unfounded "fear of invasion" rhetoric conservatives have used for years to rally political support.

"The president is very clear. The community organizations and immigrant advocates are very clear," said Fernando Garcia, executive director of the Border Network for Human Rights, based in El Paso. "This is a very limited program. Not only will it not cover anybody outside the U.S., but it's also not going to cover the vast majority of people here."

Not only does Obama's order exclude recent and future arrivals, it also comes with the promise of further bolstering Border Patrol. That should add yet more deterrence to those hoping to cross, the Border Network's Garcia said.

Immigrant influx

Republicans argue similar deferred deportation programs nonetheless caused influxes of new illegal immigrants.

They point to the president's 2012 Deferred Action for Childhood Arrivals, which provides temporary legal status to some young people who arrived in the U.S. as children. It was expanded by the recent executive action. The limited scope of the program led to a widespread rumor that inspired thousands of hopeful youths and families to trek toward the American Dream and away from violence in their home countries.

In the 2014 fiscal year, the number of children who entered the country illegally more than doubled to upward of 68,000. The wave of children that overwhelmed border communities has slowed with federal officials now reporting that the number of children detained on the Texas border is at its lowest in almost two years.

Peter Spiro, an immigration law expert at Temple University in Philadelphia, said Obama's executive action is the latest in a "historical pattern" to allow the number of undocumented immigrants to swell so large that "the government has no choice but to regularize them."

Rather than quash hopes many illegal immigrants have for obtaining legal status, Obama inadvertently bolstered the possibility, said Jessica Vaughan, director of policy for the Center for Immigration Studies, a Washington D.C.-based research organization.

"The president has sent a message that makes it clear that if they come here and stay under the radar for a short period that they could get another amnesty," she said.

That might cause an increase in illegal attempts to cross the border, although most researchers said they expected a bump rather than a surge.

"The people who might come are fence-sitters, looking for an excuse," said Néstor P. Rodríguez, a sociology professor at the University of Texas at Austin. "But they're likely to come anyway."

Overall, he said, illegal immigration is seeing a yearslong decline. The number of Mexicans crossing into the United States has plummeted, while the share of immigrants making the costly journey from Central America has risen, he said.

Rodriguez noted that research shows migration spikes when economies collapse or violence erupts in people's home countries. Migrants are less influenced by political speeches, he said.

"It's not like you hear the news and get up and walk out the door," Rodriguez said, noting coyotes always circulate rumors designed to entice customers. "Undocumented migrants pay $7,000 or more to smugglers to come here. You don't come by yourself. It's very dangerous and risky."

An education campaign by the United States and Latin American governments to make clear that the new program is limited would help prevent a new surge, said Ali Noorani, executive director of the nonpartisan immigrant advocacy organization the National Immigration Forum in Washington, D.C. Noorani, Spiro and Vaughan all attributed the decline in child immigrants, in part, to the president making appearances this year on Spanish-language television.

The misinformation Fernando Garcia worries more about is the potential for fraudulent attorneys and notaries to claim they can help undocumented immigrants obtain legal status or work permits, when the process has not yet been implemented or may not even exist.

Weary with surges

Many residents along the border express weariness with the cycle of border surges, regardless of what spurs them, as well as the political sparring that follows.

"My belief: Nothing's going to change," said Hidalgo County Pct. 3 Constable Lazaro "Larry" Gallardo.

He no longer sees dozens of women and children huddled on the Rio Grande, scanning the banks for a U.S. Border Patrol agent, who they hope will lead them into a new American life, as was commonplace last year. Caravans of buses filled with hundreds of children being taken to detention centers no longer cross through town multiple times a day.

But ranchers still find the bodies of those who took riskier routes to avoid the growing force of Border Patrol and law enforcement sent to secure the border. Police still find once-hopeful immigrants kidnapped by a rival smuggler and held hostage in crowded safe houses. Community leaders still seek to assuage community fears of declining safety as rival cartels raid each others' stash homes.

Many border residents have ties to Mexico stretching back generations, leaving them wondering whether families might be reunited and skeptical about whether political bickering will subside.

"The majority of the citizens here, and to some degree the immigrants here, we're all in a state of confusion," said Susan Kibbe, executive director of the South Texans' Property Rights Association and a rancher. "It's time for the new Congress to hammer this out in a way that serves all of us."