"The cartels are more likely to go after local police," Grayson said. "You threaten an FBI agent and it does sound alarm bells across Washington. The same with Drug Enforcement Administration."
Phil Jordan, former DEA intelligence chief along the U.S.-Mexico border, believes Guzman may have been behind the threats in order to divert law enforcement attention away from the heavily-travelled drug corridor between El Paso, Texas, and Juarez, Mexico. But he doesn't think Mexican cartels will actually target American law enforcement.
"Let me tell you something about the cartels – whether they're from Colombia or Mexico or Russia – they do not under any circumstances want to spend time in American jails," Jordan told ABCNews.com. "The cartels are not going to take us on on American soil. They have cells all over the U.S. but they don't want that type of attention."
Jordan added, "Chapo Guzman is no dummy. If he can put out stuff like that so we can send reinforcements to the Nogales sector, he knows we'll have to send people from the Texas border to help and you'll see an increase in drug loads moving through Texas."
The Los Zetas criminal organization, the Sinaloa Cartel's chief rival, had previously operated in the Nogales area, but Grayson said Guzman has probably taken over control of operations there in recent months.
"El Chapo has really enjoyed a comeback in the last several months," Grayson said. "These threats are just a general flexing of the muscles by the cartels. El Chapo has to be emboldened by the fact that Los Zetas find themselves on the defensive."
The Sinaloa Cartel is one of the biggest suppliers of cocaine to the United States. Its members are well-trained and well-armed, according to experts. About 90 percent of all the cocaine consumed in the United States passes across the Mexican border.
The booming drug trade has fueled powerful drug armies willing to take on Mexican police and even the army, and have no qualms about terrorizing civilians as well.
In the northern Mexican state of Sonora, across the border from Arizona, 126 drug-related homicides have been reported so far this year.
This week, with more than 40 deaths attributed to drug violence, including 12 federal police officers ambushed on Monday.
Last week, gunmen killed 16 people in Ciudad Madero, and 19 men were shot dead at a drug rehab center in Chihuahua.
Across the border from El Paso, Texas, in Ciudad Juarez, the body count has soared to nearly 1,200 this year. An estimated 2,700 were killed in 2009, a number that neared that year's death count for civilians and U.S. and coalition soldiers in Afghanistan, according to the United Nations.
"The cartels are feeling their oats now," Grayson said.