In 2017, Martin Shkreli was convicted of securities fraud and sentenced to prison. The transcripts of his jury selection show that there was some difficulty in finding jurors who would admit to being able to judge the case fairly.
Here are some examples of the jury selection interviews.
So, my question is: Under US law, what happens if it is practically impossible to assemble a jury, either because no-one will admit to being impartial, or for any other reason?