Of about 100 potential jurors, 45 were interviewed by Judge Brian Cogan on Monday, of which 17 were dismissed and no one yet impaneled.
Mr Heroy estimates the trial will cost USA taxpayers "more than US$50 million", a price tag that includes protection programmes for at least some of the hundreds of witnesses expected to testify. Another was sent home after she said she couldn't be impartial, saying, "I feel very bad about drugs".
Jurors also will be escorted to and from the courthouse by federal officers and sequestered from the public while inside. For the most part, he did not make eye contact with potential jurors, who were brought within about 10 feet (three meters) from him for individual questioning.
It's a bagel with cream cheese, lox and capers, he replied.
"El Chapo" is also charged with using firearms in running a drug trafficking and money laundering operations, while making $14 billion in cash from the sale of narcotics throughout the United States and Canada.
Guzman has been branded the world's biggest drug lord since Colombia's Pablo Escobar, who was dubbed "The King of Cocaine" and was one of the wealthiest men in the world until police shot him dead in 1993.
Prosecutors say the USA government is seeking a $14 billion forfeiture order as part of the case.
Guzman pleads not guilty.
Guzman, 61, formerly led the Sinaloa Cartel, named after its base in the Mexican state of Sinaloa. His co-defendant Ismael "El Mayo" Zambada remains at large, and violent drug trafficking continues unabated in Mexico. Guzman sat at the defense table listening through an interpreter and wearing street clothes - a dark suit and a white shirt with an open collar - instead a jail uniform for the first time since he was extradicted to the United States early previous year.
Guzman was extradited to the United States in January 2017 on an indictment that detailed his alleged reign over a merciless trafficking organization controlled through murder and torture. In 2016, an average of 174 Americans died every day from drug overdoses. He spends 23 hours a day in his cell.
The only visitors he is allowed are his lawyers and twin, seven-year-old daughters, from whom he is separated by thick glass. The judge has banned his 29-year-old beauty queen wife, Emma Coronel, from visiting. As jury selection is being held behind closed doors, she did not attend Monday.
Federal authorities have imposed high security to prevent Guzman from slipping away yet again. He was rearrested in 2014 only to escape 14 months later from a tunnel dug into the prison.
In a secret meeting with actor Sean Penn which the Hollywood star wrote about in Rolling Stone magazine in 2016, Guzman boasted: "I supply more heroin, methamphetamine, cocaine and marijuana than anybody else in the world". This time, Mexico chose to wash their hands and put him on a plane.