Justice Minister Ayelet Shaked (Jewish Home) warned Netanyahu against calling early elections, saying that doing so would bring down a right-wing government.
The ultra-Orthodox parties have agreed to support the budget if the conscription bill passes an initial parliament reading for now, with a final vote postponed until the summer session.
Netanyahu separately called on all coalition partners - "first and foremost Defence Minister Avigdor Lieberman" - to remain in the government.
Under Tuesday's compromise, the five-seat secular nationalist Yisrael Beitenu party, which opposed the bill, will be allowed to vote against it. Though he has become a responsible cabinet member ("the most adult among them", we hear sometimes) and apparently not a bad minister of defense, the Russian base of his party is shrinking and one of the former members of his parliamentary faction has made a decision to form her own party thus competing with the man who once was her boss.
That having been said, the deal worked out is truly one of epic complexity, involving marathon - separate - meetings between Prime Minister Benjamin Netanyahu and various ministers to figure out ways to resolve the crisis and avoid early elections, including Finance Minister Moshe Kahlon, Defense Minister Avigdor Liberman and Education Minister Naftali Bennett.
Lieberman can climb down from his high ladder and support the new draft bill, which represents significant chareidi compromise.
Israel's lawmakers are now discussing the opposition's proposals to dissolve the Knesset.
Trump hosted Netanyahu and his wife at the White House on Monday.
Netanyahu's legal woes are the focus of the coalition crisis, with a range of politicians accusing him of allowing it to worsen to give him the option of forcing early polls.
Trump is demanding "significant changes" to the Iran deal, not just additional agreements between the United States and the European nations, and said he would pull out of the deal if those changes aren't made, Israeli officials told Axios.
Investigators last month recommended to prosecutors that Netanyahu be indicted in at least two corruption cases against him. One poll predicted Likud would win as many as 34 seats if elections were held now.
Netanyahu, who attended MIT (the Massachusetts Institute of Technology) as an impressionable college student, said one thing that makes the United States truly unique in all the world is that no matter who you are, or where you're from, you can succeed if you're talented and work hard.
Netanyahu has a chance to break the late David Ben-Gurion's record of 4,575 days in the premier's office: He would need to stay on the job until near the end of September.