(Reuters) - Scared that her 25-year-old son might die from a heroin overdose, Jennifer Stepp said she took the unusual precaution of teaching her 8-year-old daughter Audrey how to administer naloxone, an opiate overdose antidote.

"She told me, 'If something happens to my brother, I want to save him,'" said Stepp, an anti-drug activist in northern Kentucky's Bullitt County who on Saturday organized a training session in the town of Hillview for about 50 adults and children on the use of naloxone, which is given as a shot or nasal spray.

With the United States experiencing a worrisome rise in overdose deaths from opiate drugs including heroin, morphine and prescription painkillers such as OxyContin, Stepp argues naloxone should become as common as the EpiPen shot for certain life-threatening allergies.

Stepp is part of a national push by some health advocates to put naloxone, also known by the brand name Narcan, into the hands of not only paramedics, police and pharmacists but also addicts' relatives to try to prevent deaths from opiate drugs.

People ensnared in America's opiate epidemic are primarily white, with many from rural or small-town settings like in Bullitt County although many others can be found in affluent suburbs.

Such overdoses killed 23,150 people in the United States in 2013, the most recent year for which national figures were available, according to the U.S. Centers for Disease Control and Prevention, while deaths from heroin alone quadrupled to 8,257 that year compared to the 2,080 a decade earlier.

Naloxone counteracts the effects of opiate drugs on brain receptors that can lead to slowing respiration, coma and death during an overdose, restoring normal breathing within minutes.

The lack of wide availability makes it important for families with people who use opiates, legally or illegally, to secure their own naloxone supply, Stepp said.

When people call a 911 emergency line to report an overdose, she said, police usually arrive first, before medical personnel. Often they do not have the drug, though many departments have started training officers in naloxone use.

"While you're waiting for the ambulance the person you're worried about is not getting enough oxygen," Stepp said. "Seconds count."

She said her son recently completed drug rehab treatment, a vulnerable time for overdoses.

DOES NALOXONE ENCOURAGE ABUSE?

Critics contend naloxone may encourage drug abuse by reducing the risks.

Karyn Hascal, president of The Healing Place, a drug treatment center in Louisville, Kentucky, is conflicted on the issue. Hascal said first responders should have naloxone and be trained to use it, but worries that users could become too "laid back" if they think they can always be revived. Hascal said users need to know they must seek treatment.

One potential barrier to broader naloxone access is its cost: about $80 per dose for the nasal spray, $40 for the shot.

As of September, 43 of the 50 states, as well as Washington, D.C., had laws to increase layperson access to naloxone, but they are a patchwork and ease of access varies, according to a report by Corey Davis and Derek Carr of the St. Paul, Minnesota-based Network for Public Health Law, which provides legal assistance and training on public health issues.

For example, Ohio provides broad civil and criminal immunity to providers of naloxone, while Iowa does not.

The New York-based Harm Reduction Coalition, an advocacy group on drug-use issues, said it knows of no lawsuits or prosecutions over dispensing naloxone, but the liability threat acts as a "symbolic barrier" to some doctors, according to Daniel Raymond, the group's policy director.

There is also a lack of awareness. Many people who have opiate users in their families do not know about naloxone even though it has been around since 1971, Raymond said.

Hascal said she agrees some families might need naloxone, but expressed concern about training children to administer it, wondering about the effect on a child if a revival attempt fails. "That should be done by a first responder," Hascal said.

Daniel Bigg of the Chicago Recovery Alliance, which since the 1990s has trained people to use naloxone, said the stigma about drug abuse is one of the biggest challenges to both overdose prevention and addiction treatment.

"We use a toxic mix of moralizing and stigmatizing," Bigg said of Americans. "It silences the exchange of views, and it kills."

(Reporting by Mary Wisniewski in Chicago; Editing by Daniel Wallis, Ben Klayman and Will Dunham)