If demographics are destiny, it makes sense that this long-simmering tension is reaching a rolling boil. While Haredim account for less than 10 percent of Israel’s seven million citizens, and Arabs 20 percent, their high birthrates mean that about 46 percent of today’s kindergartners come from the two groups, growth that is “challenging the basic formula” of Israeli society, according to Aluf Benn, editor of the left-leaning newspaper Haaretz.

“These groups don’t want a larger slice of the pie, they want a different recipe,” Mr. Benn said in an interview. “If Israel defines itself as a Jewish democratic state, the Arabs would do away with the Jewish part, and the ultra-Orthodox at least in their dream would get rid of the democracy. They respect the authority of the rabbis.”

Einat Wilf, one of five lawmakers who served on the committee, said that the solution was not a universal draft, but an acceptance that “the people’s army” is a fiction — and a reworking of benefits accordingly.

“We have to accept the fact that 64 years ago they did not want the state to come about, and they still have no faith in the structures of the state,” Ms. Wilf said, referring to the utra-Orthodox and Arab citizens. “Solidarity is a two-way street. The state will guarantee everyone the absolute minimum, but beyond that the state will reward people who give, not just people who take.”

Mr. Netanyahu met Thursday afternoon with Mr. Mofaz and leaders of other parties in the coalition to begin hammering out a compromise. Ze’ev Elkin, chairman of the coalition, said earlier in the day that he thought that the gaps between their positions could be bridged, saying that neither was opposed to personal sanctions on those who do not serve. Some Kadima members said Mr. Mofaz had said he would quit the government if a deal was not done by Monday.

Though one Haredi rabbi, Avraham Eisenstein, issued a statement on Wednesday saying that no yeshiva student would be drafted, “be it his will or against his will,” a leader of the ultra-Orthodox Shas Party indicated a willingness to accept the principles, if not the particulars, of the committee.

“The practicality of implementing any law depends on it being spread out and on processes that take place slowly, not in one blow,” the leader, Ariel Attias, said in a radio interview. “We want and are willing for processes to take place, some of them very painful, but don’t pretend that this is being nice.”