According to The Monitor ("Serving the Rio Grande Valley Since 1909"):

Illegal immigrants have started surrendering to local Border Patrol agents after crossing the Rio Grande, convinced they’ll be released by Immigration and Customs Enforcement, which recently turned hundreds of immigrants loose to save money.

In preparation for the sequester — federal spending cuts forced by Congress’ inability to reach a budget deal — ICE released several hundred low-risk illegal immigrants from detention centers last month and placed them on supervised released instead. The news reached illegal immigrants preparing to cross the border.

“These are people that are just voluntarily turning themselves in to our agents with the expectation they’ll be released,” said Border Patrol Agent Paul Perez, president of the Rio Grande Valley union of the National Border Patrol Council. “When you cross with the expectation that you’ll be released, there’s no need to hide, there’s no need to run. You just look for a uniformed agent and turn yourself in.”

ICE stopped releasing immigrants after the cost-cutting move sparked public outcry.

On March 3, many illegal immigrants detained at Border Patrol’s McAllen Station asked about being released, said agency spokesman Enrique Mendiola. Apparently, the illegal immigrants heard that ICE released detainees and wanted similar treatment.

“We make the arrests, we do the processing and then we hand them over,” Mendiola said, adding that Border Patrol doesn’t handle long-term detention — or release.

Neither Perez nor local rank-and-file agents knew how many illegal immigrants voluntarily surrendered with the expectation ICE would release them.

There are some who deny it.

McAllen-based immigration attorney Carlos M. Garcia, who regularly visits the East Hidalgo Detention Center in La Villa and the Port Isabel Detention Center in Los Fresnos, said he hadn’t heard about any such cases.

“I think in general they would rather avoid detection or contact with the government,” Garcia said.

The behavior described by Border Patrol agents at the McAllen Station seems unlikely, said John-Michael Torres, a spokesman for La Unión Del Pueblo Entero, which advocates for immigration reform. Generally, immigrants cross the border looking for work and attempt to avoid scrutiny from government authorities.

However....

Some rank-and-file agents have speculated that illegal immigration might increase thanks to the ICE cost-saving program.

In December, agents arrested 2,758 people, according to McAllen Station data released by Customs and Border Protection. The number held steady during January, when agents arrested 2,815 people.

In February, though — the month ICE began releasing illegal immigrants to save money — agents arrested 4,777 people, according to CBP data. What caused the spike isn’t clear.

Typically, CBP doesn’t release station-specific numbers, but The Monitor obtained internal data from the McAllen Station. Mendiola confirmed the monthly statistics.

There may be cuts in border security:

Other parts of the sequester, which will cut $85 billion in federal spending, will further affect border security, Perez said.

In the Rio Grande Valley Sector, agents typically work 10-hour shifts. To save money, they might start working eight-hour shifts starting next month, Perez said. Additionally, agents might face 14 furlough days — essentially unpaid vacation. Overtime would drop severely.

“The coyotes and those folks listen to what’s happening here,” said U.S. Rep. Henry Cuellar, D-Laredo. “They’re probably getting the impression, ‘Hey, there are going to be less people working. There will be less security.’”

More illegal immigrants caught, expecting quick release, Border Patrol union says (Dave Hendricks, The Monitor, March 15th, 2013)