At the heart of the scandal is an accusation by the Channel One television station that Benjamin Netanyahu, the Prime Minister, nominated Roni Bar- On, an obscure party loyalist, as attorney-general to allow a political ally of the government to escape corruption charges.
Mr Bar-On's appointment was greeted with astonishment and derision by the legal profession and senior judges, who forced him to resign after 12 hours. It was reported that two-thirds of the cabinet had never heard of Mr Bar-On, but it was the one third who knew him who voted against him.
Last week state-owned Israeli television said his appointment was made after he promised to arrange a plea bargain for Aryeh Deri, leader of Shas, a party with 10 members in the Knesset, who is on trial for corruption. In return Mr Deri promised to support the Hebron agreement, leading the scandal to be called the "Bar-On for Hebron" affair.
Mr Netanyahu and his government denied any such deal. The television reporter has yet to explain the source for her claims, but may be forced to do so by the police investigation. In general terms there is little doubt the government wanted to get rid of the previous attorney-general and replace him by somebody more malleable, but it would be surprising if they made a specific agreement with Mr Bar-On.
In its seven months in office the government has proved accident-prone and Mr Netanyahu has made several bizarre appointments. His first choice as justice minister had to withdraw, accused of making false statements to the Supreme Court. His office director was alleged to have a long record of making harassing calls to women. Other right-wing leaders are in trouble, such as Ehud Olmert, Mayor of Jerusalem, who is on trial for fraud.
Mr Netanyahu has accused Channel One of extreme bias against him.
Rafik Halabi, editor of its nightly news, said he was confident. "We will take this all the way," he said. "I'm not concerned, I'm not scared and I'm not worried. We will protect our sources, but will act within the confines of the law."
Senior members of the government appear to lack confidence in what Mr Netanyahu's kitchen cabinet - often compared to that around President Richard Nixon - might have got up to. Natan Sharansky, the Trade and Industry Minister, said yesterday: "If there was any kind of bargain, I recommend to everyone involved to admit it and resign, because this is an unprecedented crime." Avigdor Kahalani, Internal Security Minister, said: "If the affair is in fact as it appears, there is no doubt that this government has no future."
Mr Netanyahu himself called for a police investigation. But he has moved in the past few days from total denial to qualified denial, saying that if there was any deal, he did not know about it. It turns out that his own choice for the position of attorney-general - an important job in Israel, since whoever holds it acts like a special prosecutor in the US - was Dan Avi-Yitzhak, Mr Deri's lawyer, who turned down the job.
There is no doubt that Mr Netanyahu wanted an attorney-general he could control, but his political future may depend on whether he or anybody in his government ever spelt out what they expected Mr Bar-On to do for them.