The escalation of drug-related violence in Mexico — including the mass execution of 72 migrants last week — is moving a small but growing number of U.S. foreign policy hawks to call for a radical solution: send in the U.S. Army.

I’m not kidding. At first, I thought it was a joke, or the kind of overreaction that is most often confined to the blogosphere.

But, increasingly, populist local U.S. officials are seriously talking about sending in U.S. troops to end the drug-related violence that has cost 28,000 lives in Mexico over the last four years, and that occasionally spills over to the U.S. side of the border.

The U.S. military would help crack down on the drug cartels, and help stop illegal immigration and terrorism, they claim. President Barack Obama’s recent decision to deploy up to 1,200 National Guard troops along the Southwest border with Mexico has obviously not pacified them.

When I interviewed Sheriff Joe Arpaio of 4 million-population Maricopa County, Ariz., about his hard-line immigration views last week, I was ready to hear a lot of tough talk against undocumented immigrants, but I wasn’t expecting him to advocate sending U.S. troops to Mexico.

Arpaio, a darling of conservative talk shows who prides himself on having put 40,000 undocumented migrants behind bars and promotes himself as “America’s toughest sheriff,” lashed out against Mexican laws that prohibit U.S. troops from engaging in battle inside Mexico. During his years as a Drug Enforcement Administration agent in Mexico, he actively fought the drug cartels, he said.

“When I was a director there, my agents worked undercover. They were involved in gun battles. They worked with the military, they worked with the federales (police). … We were operational, approved by the Mexican government,” Arpaio said. “Why don’t we do the same right now?”

“I’m not a proponent of the Army of the United States being involved in law enforcement, but we have armies right now in Afghanistan, Iraq. … We go into other countries. Why can’t we go into Mexico with their cooperation?” he asked. Asked to elaborate, he said it would have to be done with Mexico’s approval.

Mexico’s ambassador to the United States, Arturo Sarukhan, told me that sending U.S. troops to Mexico “is a non-starter.” Another Mexican official told me that Mexicans are very sensitive about the U.S. military interventions that resulted in the annexation of Texas and California in the 1830s and 1840s, and that the presence of U.S. combat troops in the country would be politically explosive.

“The United States can continue to play a constructive role by stepping up efforts to stop the flow of U.S. small arms to Mexico — 80 percent of all successfully traced weapons in Mexico come from the United States — and speed up disbursement of $1.4 billion in law enforcement equipment under the Merida Initiative,” Sarukhan said.

My opinion: Talk about sending U.S. combat troops to Mexico is crazy. You would have anti-U.S. student demonstrations starting a day later, followed by a dead protester who would immediately become a national and international martyr, followed by resurgence of leftist guerrillas, followed by a cycle of violence that would lead to more bloodshed than the current war on the drug cartels.

What should Washington do, then? First, take a deep breath and think calmly. Mexico’s murder rate is rising fast, but as we reported in this column on March 24, according to U.N. figures it’s still about five times less than that of Honduras, Jamaica or Venezuela, and significantly less than that of Washington, D.C. The United States should not overreact.

Second, it would be a good idea for both Mexico and the United States to significantly increase their military forces on their respective borders: in Mexico’s case, to stop the drug flow, and in the U.S. case, to stop the arms and money smuggling.

And third, it’s time to start thinking about a significant expansion of the U.S. Merida Initiative.

Washington should give Mexico more helicopters, intelligence and — above all — technical assistance and training to create police academies that would help dismantle Mexico’s 2,200 corruption-ridden police forces, and replace them with more reliable ones. Everything, except sending U.S. troops.

— Andres Oppenheimer is a Latin America correspondent for the Miami Herald. aoppenheimer@miamiherald.com