But, despite those caveats, Hebrew media reported on Wednesday that the Religious Zionism party has decided to back the bill, meaning a considerably easier ride through the Knesset.
Party leader Bezalel Smotrich, the finance minister, is expected to support the legislation following consultations with senior rabbis affiliated with his faction.
The rabbis are said to have expressed concerns over the IDF's ability to take in more significant numbers of Charedi troops and stressed the importance of keeping the governing coalition intact.
As the second largest party in the coalition, Religious Zionism's support would mean the bill is likely to pass the Knesset.
Votes from Likud, Religious Zionism and the two Charedi parties, Shas and United Torah Judaism, would give the law a majority of four in the chamber even if no other coalition members or opposition MKs voted in favour.
The government is also understood to be considering an amendment to a clause allowing some Charedim to meet the draft quota by serving in non-military roles, such as in the Shin Bet, to secure Smotrich's backing.
However, supporting the bill could come at a political cost for the finance minister, given the nature of his party's voting base.
Religious Zionists have one of the highest enlistment rates in the country and place great emphasis on military service, with many strongly opposing any exemption for young Charedi men.
