FALFURRIAS, Texas — Texas sheriffs are fuming over Gov. Rick Perry’s failure to consult them before dispatching 1,000 National Guardsmen to bolster the border with Mexico.

Local officers say they’ve confronted the daily fallout from a porous border and broken immigration system for decades, while the Guard troops will lack authority to make arrests and are unfamiliar with the terrain. They say even a fraction of the millions of dollars Perry is spending would be better used to supplement the coffers of places like Brooks County, an area so starved of money that it relies on unpaid volunteers to maintain order in a territory the size of Rhode Island.

It isn’t easy. Last weekend, Brooks Deputy Sheriff Kenneth Ennis found himself in a 100 mile-per-hour chase at 4:45 a.m. tailing a tan pickup suspected of just having just dropped off a load of undocumented immigrants. The truck raced down a desolate road before slamming into a wire fence.

“Sheriff’s Department!” Ennis screamed as he jumped out of his Chevy Defender and ran toward the immobilized vehicle, drawing his .40 caliber Glock pistol as the driver took off on foot into the darkness. “Stop!”

Perry’s July 21 surge announcement has been widely viewed as an attempt to augment his profile as he rides out his third and final term and contemplates another run for the White House. His state has been in the spotlight in recent months as a record wave of unaccompanied children, mostly Central American, crosses the border.

The debate over how to stop an influx of undocumented children and adults has divided the governor’s fellow Republicans. They’re balancing attempts to look tough on immigration without alienating Latinos, whose support they need at the ballot box.

National Guardsmen, set to arrive this month, will work “seamlessly and side by side” with civilian law enforcement to combat activity by drug cartels and human traffickers, Perry said. It’s part of a years-long effort that’s needed due to the federal government’s failure to seal the border, he said.

Details on what the Guard will actually do remain elusive. At a hearing last week in Austin, state lawmakers received vague responses about the mission’s goal and duration when pressing Maj. Gen. John F. Nichols of the Texas National Guard. The Texas Military Forces, which oversee the Guard, declined to provide more details, citing security concerns. News reports have pegged the operation’s cost at $12 million to $17 million per month.

“That’s money really thrown away,” said Sheriff Omar Lucio, a Democrat who oversees Cameron County, which borders Mexico on the Gulf Coast. “Why would you spend millions on something like that that’s not going to work?”

County officers call the surge a temporary Band-Aid that will provide only short-term relief, if any. At the Sheriffs’ Association of Texas meeting in late July, the top cops of the state’s 254 counties voted unanimously on a resolution calling on leaders in Austin and Washington to include them in border-control planning.

“This idea of using the National Guard was never discussed with our sheriffs,” said Don Reay, executive director of the Texas Border Sheriff’s Coalition.