Prime Minister Benjamin Netanyahu is set to meet Monday night with Yisrael Beytenu leader Defense Minister Avigdor Lieberman, who threatened to quit the government if the legislation passes.
The amendment to the IDF draft law, which was proposed by Shas MK Yoav Ben-Tzur, would solicit state recognition of Torah studies to being equal to military service, essentially ensuring exemptions to all yeshiva students.
Members of the Likud party have spent the day trying to convince Lieberman to toe the coalition's line and accept the draft law amendment, while offering to make changes to the legislation based on notes from the Defense Ministry.
Some Likud officials said it was made clear to Lieberman that if elections are called now, he is not guaranteed to keep the defense portfolio in the next government as well.
Netanyahu held a long meeting on Monday evening with Knesset Speaker Edelstein and Minister Yariv Levin, who is the liaison between the Knesset and the government, in an effort to find a solution to the crisis.
Many in the political system, however, claim the train has already left the station and elections were only a matter of time.
The 20th Knesset might be dissolved this week or alternatively only after the Passover hiatus. "Either way, it appears inevitable," a coalition official said.
"It's a very dramatic 24 hours for the future of the government," a Likud official said.
On Tuesday, the Ministerial Committee for Legislation is due to meet to discuss Yisrael Beytenu's appeal against the ultra-Orthodox parties' draft law amendment.
Immigration Minister Sofa Landver, who submitted the appeal on behalf of her party, will land at Ben-Gurion Airport at 2pm Tuesday after a few days abroad and head straight to the Knesset to explain the reasons behind the appeal.
After the Ministerial Committee for Legislation rejects the Yisrael Beytenu appeal, the legislation will be brought to a preliminary reading at the Knesset plenum.
Knesset Speaker Yuli Edelstein has also approved to raise to a vote a proposal to dissolve the Knesset, which was submitted by members of the opposition. If passed, the elections for the 21st Knesset will take place within 90 days.
Amid the tense atmosphere in the Knesset, officials in the legislature have already begun discussing possible dates for the elections.
Netanyahu prefers a quick process, which would see the elections held in June. But some of his coalition partners prefer to postpone the elections as much as possible, arguing that the municipal elections are scheduled for November and the timetable should be planned with that in mind.
To set a date, representatives from all Knesset factions will meet at the Knesset speaker's office and vote for their party's preferred date. Each party's vote will be worth the number of seats it currently has in the parliament. A majority of 61 MKs will determine the date for the elections.