Beavers has pleaded not guilty to charges that he diverted campaign money for personal use without reporting it.
Jury selection began Tuesday.
Defense attorneys have asked the judge for a new jury pool because the current one contains only a few African-American females and no African-American males.
"I have never seen a case where I represented a Black man defendant and they send up 50 jurors! Fifty! Fifty jurors! And not one single Black man," said Sam Adam, Beavers' attorney. "Now don't tell me that was an accident."
The judge said if there's evidence a mistake was made in selecting the jury pool, he would reconsider the defense request for a new jury pool.