The political crisis comes as Netanyahu is battling a series of corruption allegations. Opponents, however, have accused Netanyahu of orchestrating the impasse to trigger an election that could bolster his standing before a possible indictment on influence-peddling charges.
In the past, the parties have compromised over the issue, but at least one coalition partner suggested Netanyahu was not invested in preventing the government's collapse.
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.
Earlier on Monday, the government's Ministerial Committee for Legislation voted in favor of the bill following overnight talks between Netanyahu and ultra-Orthodox coalition partners for an agreed version of the bill.
Ultra-Orthodox parties that help underpin Netanyahu's government had demanded a vote on the conscription legislation before passing the budget.
Finance Minister Moshe Kahlon, in turn, said he will pull his party (Kulanu) from the coalition if the budget fails to pass this week.
Israeli Prime Minister Benjamin Netanyahu said Tuesday that his coalition struck a compromise to avoid taking the country to early elections. However, Iranian President Rouhani has said he wouldn't be the first to abandon the deal and has informed the United Nations Atomic Energy Agency that it will continue to comply with the deal's terms. The opposition Zionist Union is opposing this, however, because polls show them losing a substantial number of seats.
"We'll vote against the enlistment law", he pledged. "It's painful, just painful that the elections have been canceled".
In order to make us believe that the consideration about his personal future isn't on his mind at all, he may have got Lieberman to be the bad boy for which he'd be amply rewarded.
"To expect that Yisrael Beytenu will support this legislation is absurd".
Lieberman does not support the bill, but his comments on Monday left the government with some room for manoeuvre in the coming weeks.
Military service for ultra-Orthodox men is one of the most fraught topics in Israel and looked to undermine Netanyahu's coalition government, which has 66 out of the 120 lawmakers. Yair Lapid's Yesh Atid is projected to do well, but not well enough to form a government, because the ultra-Orthodox won't sit with him and it's not likely that anybody can form any government in Israel without the haredim.
Haredi groups have been opposed to conscription for a wide variety of reasons, among them pacifism, the importance of preserving Jewish religious studies, and the integration of men and women in the Israel Defense Force (IDF) which flies counter to the sequestration of unmarried men and women in Orthodox Judaism.