"In 2017 the High Court struck down legislation allowing the blanket exemption of Haredi men from military service as discriminatory, and gave the government one year to pass new legislation that would boost levels of ultra-Orthodox military enlistment. Due to numerous elections that occurred in the interim, it has since given the state multiple extensions to that deadline.
Since the law that the High Court struck down could not itself be extended beyond June 2023, the current cabinet passed a government resolution that month to legally enable the military not to draft Haredi men until the end of March 2024, in order to give the government time to formulate a new arrangement for ultra-Orthodox military exemptions that would comply with the High Court’s 2017 ruling." https://www.timesofisrael.com/ag-says-haredim-face-military-draft-if-no-legislation-by-april-seeks-deadline-extension/
"Recent polls show that Israeli Jews—including majorities on the political right and center right—now overwhelmingly oppose blanket Haredi exemptions. A February survey found that an astonishing 73 percent were against exemptions—up 11 points from November. A poll released this week similarly found that 73 percent of Israeli Jews, including a majority of people who voted for the Netanyahu government, oppose the billion-shekel subsidies to Haredi institutions that are included in the government’s current budget proposal.
With the public incensed at what many see as Haredi privilege, Netanyahu is facing revolt within his ranks. Most notably, Defense Minister Yoav Gallant has publicly called for an end to the exemptions and said he will not support any legislation on the matter that is not also approved by Benny Gantz, a centrist opposition lawmaker and rival to Netanyahu who sits in the country’s war cabinet. But any Haredi-draft bill that satisfies Gantz and Gallant is unlikely to satisfy the Haredi parties, who perceive enlistment as a threat to their cloistered way of life. And if no new legislation is passed, the IDF will be required to begin drafting the ultra-Orthodox on April 1." https://archive.is/V7Lgw
Currently, Netanyahu's coalition has 64/120 members of the Knesset, with 18 members of his coalition belonging to "Ultra Orthodox" parties.
Coalition breaking down is anything that leads to the dissolution of the 37th Knesset. https://en.idi.org.il/articles/6111