Joe Amendola and Karl Rominger gave a sealed motion to Judge John Cleland during jury selection. They said they hadn't been given enough time to prepare.
"We told the trial court, the Superior Court and the Supreme Court we were not prepared to proceed to trial in June due to numerous issues, and we asked to withdraw from the case for those reasons," Amendola said.
The judge denied the request after a discussion in his chambers.
Sandusky, a former Penn State assistant football coach, was convicted Friday on dozens of child sexual abuse charges. His lawyers had said a delay was needed because a key member of the defense team had a scheduling conflict and a lengthy grand jury investigation had inundated them with documents and other materials.
Rominger also said Saturday that prosecutors told him on June 14, during the trial's first week, that they obtained a tape of the allegations made by adopted son Matt Sandusky that he also was a victim of abuse by Sandusky. Rominger declined to comment on the details of those allegations but said calling him to the stand might have prompted a mistrial.
He said Matt Sandusky had been expected to be an important witness for the defense, and when such a defense witness becomes a prosecution witness, that can result in a mistrial. The Matt Sandusky evidence and potential testimony was why the prosecution's case was held open during a surprising day off from the trial on June 15 and did not rest until Monday, he said.
After a swift trial and less than two days of deliberations, the jurors found Sandusky guilty on Friday, drawing raucous cheers from hundreds of onlookers outside the courthouse.
Over the course of the two-week trial, eight men testified about abuses that ranged from kissing and massages to groping, oral sex and anal rape.
Afterward, Sandusky's attorney, Joe Amendola, addressed the media with a vocal crowd behind him.
"Essentially the sentence that Jerry will receive will be a life sentence, just due to the length of it," he said, which was met with more cheers from the crowd.
The verdict is not the end of the scandal, which took down legendary head coach Joe Paterno and deeply shook the state's most prominent university. It will play out for years in courtrooms and through a set of ongoing investigations.
The Associated Press contributed to this report.