The laborious task of selecting a jury for the Clemens retrial resumed Tuesday and might not be done by the end of the week, with the judge and lawyers for both sides parsing prospects’ thoughts on topics as disparate as Barry Bonds and Lance Armstrong, Twitter, and the reputation of the Justice Department.

“To be completely honest, I dislike Barry Bonds . . . Truthfully, I believe he actually did it. I believe he used drugs,’’ said one man, a graphic designer who was asked to return after he expressed neutral feelings about Clemens.

The court is narrowing the initial jury pool of 90 down to 36, from which to select the final 12 jurors and four alternates who will decide whether Clemens lied when he denied using steroids and human growth hormone before a US House committee in February 2008. The extra 20 are needed because Clemens’s lawyers are allowed to strike 12 and prosecutors, eight - without giving any reason. By the end of the second day, only 32 Washingtonians had been questioned, with 15 - 11 women and four men - meeting the initial approval of US District Judge Reggie Walton.

Jury selection will continue at least through Thursday. Even the judge’s “10-minute break’’ in the morning ended up lasting 25 minutes.

“Things aren’t going as fast as I thought,’’ Walton said in the afternoon.

Finding potential jurors without some preconceived opinion about the case - or whether it’s worth the time and expense for the government to pursue it - has been challenging. Among those who were excused was the woman who told the judge: “I feel like I know too much.’’ She said she had discussed the case with friends and added: “I frankly question the legitimacy of bringing this to this court.’’

It was during questioning of one potential juror that Clemens’s attorney Rusty Hardin raised the issue of whether Clemens truly “voluntarily appeared’’ before Congress. Clemens was not subpoenaed to testify at the 2008 hearing, and the government has always maintained that he testified on his own will.

Clemens, wearing a dark pinstriped suit and red tie, remained silent during the proceedings, listening to the questioning and often looking at notes.