The judicial official spoke on condition of anonymity because he was not authorized to talk to the press.
However, critics believe the resignation was prompted by widespread irregularities.
"The violations were blatant, and he couldn't bear more, so he resigned. Don't believe what is said about his health condition," said Hossam Eissa, professor of law in Ain Shams University and a leading opposition member. "Half of the people will not recognize this constitution."
In an interview with daily al-Masry al-Youm, a senior member of the committee, Mahmoud Abu-Shousha, warned the opposition "not to exploit the sickness of the man and describe his resignation as caused by what they consider violations in the first round."
Rights groups and opposition say they filed complaints of violations including replacing judges with employees. Egypt's Justice Ministry ordered investigation into allegations.
Many of the country's judges boycotted overseeing the referendum, though the law requires that each polling station must be supervised by a judge. The boycott is a protest against Islamist President Mohammed Morsi's actions which judges.
The latest branch of judiciary that decided to boycott is the administrative prosecution union. At a news conference on Wednesday, they protested what they called the "abduction" of the Supreme Constitutional Court, which Islamists have accused of conspiring against the referendum. Islamists held a sit-in for weeks to prevent members from convening.
One of the Muslim Brotherhood's allies, Gamaa Islamiya, which once waged a terror campaign against the regime but later renounced violence, said in a statement, "the Supreme Constitutional Court is now a clear enemy of the presidency and the constitution," warning the court against issuing any verdicts that would hinder the vote, else, "it will be waging an assault against the popular will."
The resulting shortage of supervisors has added to doubts about the referendum. The first round was held on Dec. 15 and the second round is scheduled for Saturday.
El-Balshi had himself threatened to boycott following deadly clashes between liberal and Islamist demonstrators earlier this month, one of several incidents that have increased the sense of crisis in Egypt since Morsi last month issued a decree giving himself wide-ranging powers.
Morsi rescinded the decree, but his move set the scene for further polarization when an Islamist-dominated constitutional drafting panel rushed through the draft opposed by liberal parties, secularists, Christians, and many Muslims skeptical of the Brotherhood.
The constitution received 56 percent of the vote in the first round of the referendum. The Brotherhood says the opposition needs to respect the voter majority. Its critics say the process was rushed, the vote was rife with irregularities, turnout was a low 32 percent, and that a constitution needs consensus, not just a simple majority, to gain legitimacy.
- AP