Mr. Lieberman is known to be cunning, so many Israelis suspect that his real motivations are hidden — maybe a personal vendetta against Mr. Netanyahu or a cynical ploy to gain more seats in the Knesset in a new election. But sometimes it is useful to take politicians at face value: Mr. Lieberman, who was defense minister when that bill was written, is committed to passing it and sees no reason to make it acceptable to Haredi parties.

But why he is doing this now, rather than during the last government, may have to do with larger changes to Israel’s political landscape, in particular the opportunity to redraw the map of political rivalries.

For many years, the left has been the usual punching bag for right-wing politicians who wanted to galvanize their base. The truth is that leftists, known in Hebrew as smolanim, are disliked by most of the Israeli public. They are associated with a failed peace process, with weaker security policies, with naïveté. In Israeli politics, “smolani” is often synonymous with untrustworthy and unpatriotic.

That trick is getting old. The Israeli left is defeated and marginalized. The public long ago moved rightward. The last election was predominantly fought between Likud and an upstart center-center-right party called Blue and White. The old parties of the left collectively took only 10 seats. Yes, “smolani” is still hurled as an insult at potential rivals, but with less passion. The right dislikes leftists — but there is not much left to dislike.

Maybe this is why Mr. Lieberman has decided to shift gears and go after the Haredi parties.

In fact, the Haredim are even more disliked than leftists: According to polling from the Jewish People Policy Institute, where I work, just 20 percent of Jewish Israelis say that they make a “very positive contribution” to Israel, while almost half say their contribution to Israel is “negative.”

Haredim are disliked not only because they don’t serve in the military and because their politicians hold the government coalition hostage, but also because their participation in the work force is low and they pay less in taxes than other communities. And, of course, because they are different. They wear black hats and live in segregated neighborhoods, and seem radical, outdated and sometimes just plain weird.

Speaking on Tuesday, Mr. Lieberman said: “I am not against the ultra-Orthodox public. I am for the State of Israel.” He added, “I am for a Jewish state but against a religiously coercive state.” As he tries to convince voters that he has stymied coalition talks out of principle, not self-interest, he is now bringing up other issues that relate to the ultra-Orthodox beyond military service: closing stores on the Sabbath, Haredi boycotts of factories that operate on the Sabbath and the rabbinical use of DNA tests to verify the Jewishness of Russian immigrants, and more. These are precisely the policy areas where the Haredim have exercised their political power — and where they are unpopular with much of the public.