US prosecutors have accused Mr Shkreli, dubbed the "pharma bro," of running a Ponzi-like scheme at his former hedge fund and a drug company he once ran. Shkreli has pleaded not guilty to charges of securities and wire fraud.
The difficulty of finding a jury became apparent on Monday, with potential jurors variously describing Mr Shkreli as "evil" and a "snake." More jurors cited the length of the trial, expected to last up to six weeks, as a hardship.
The ensuing headlines prompted Shkreli's lawyer, Benjamin Brafman, to ask US District Judge Kiyo Matsumoto in Brooklyn on Tuesday morning to declare a mistrial. She refused.
The trouble continued Tuesday, as Ms Matsumoto asked potential jurors left over from Monday whether they had been exposed to negative media reports about the previous day. Several who said they had were dismissed.
Mr Shkreli, 34, rose to fame in 2015 by raising the price of anti-parisitic drug Daraprim to $750 a pill, from $13.50, when he was chief executive of Turing Pharmaceuticals. The move sparked outrage among patients and U.S. lawmakers.
Mr Shkreli's upcoming trial is not about Turing but about Mr Shkreli's management at his previous drug company, Retrophin Inc, and the hedge fund MSMB Capital Management between 2009 and 2012.
Prosecutors said Mr Shkreli lied about MSMB's finances to lure investors and concealed devastating trading losses from them. They said he paid the investors back with money stolen from Retrophin, which he founded in 2011.
Tuesday's jury questioning suggested Turing might come up anyway. One juror, a pharmacist, was dismissed after saying he was familiar with the company, and that he would compare any testimony about drug pricing to his own knowledge.
Manufacturer of Daraprim, Martin Shkreli. Source: AAP, Twitter
Mr Shkreli himself may have complicated the jury selection. While most criminal defendants lie low, he has sought public attention since his December 2015 arrest, lashing out at critics and boasting of his wealth on social media. He was banned from Twitter in January for harassing a journalist.
One juror was dismissed on Tuesday after saying he was familiar with Shkreli's Twitter account.
"Unfortunately, the Twitter history is just horrific," Mr Brafman said.
