JERUSALEM — In a trio of new polls, Israelis have declared what they think of the bribery case against Prime Minister Benjamin Netanyahu, and the answer is roughly the same as what they think of Mr. Netanyahu himself: About half think he should step aside. His right-wing supporters overwhelmingly think he should stay.

Mr. Netanyahu’s Israel is as polarized as it has been in generations, and under his lengthy tenure, the national conversation has become steadily more toxic. Now, as the prime minister awaits a possible criminal indictment, his efforts to cling to power could pose even greater strains on a society that already seems at risk of tearing itself apart.

“Imagine if, in the next few weeks, there is a justified case for Israel to go to war,” said Shlomo Avineri, a professor emeritus of political science at the Hebrew University of Jerusalem. “Half of this country would think Netanyahu’s position was impacted by his legal situation. That is unacceptable. Political decisions are sometimes existential in Israel. If we had to go to war, the decision would be contaminated for a lot of people.”

Mr. Netanyahu has dismissed the police recommendations to charge him as “slanted” and “full of holes, like Swiss cheese.” The attorney general, Avichai Mandelblit, praised the police on Thursday, in his first public remarks on the recommendations. The state prosecutors and the police, he said, had worked with the goal of “preserving the rule of law in Israel, turning over every stone in order to bring the truth to light.”