Habayit Hayehudi only won three seats in the election, but the party could end up splitting and becoming even smaller.
Party chairman Daniel Herschkowitz is under enormous pressure to quit the Knesset when he becomes a minister in the new government, to allow the next name on the party list - former MK Nisan Slomiansky - to enter the Knesset. But so far, Herschkowitz has refused to give up his seat in the parliament.
Top party activists and interest groups are concerned that if Herschkowitz becomes a minister and his No. 2, MK Zevulun Orlev, a deputy minister, Habayit Hayehudi will only have one active MK, Uri Orbach, to fight for the party's causes in the Knesset.
Slomiansky has had success in fighting for funding for the party's interests in the Knesset Finance Committee.
The heads of religious-Zionist institutions have been signing petitions, writing letters and phoning Herschkowitz in an effort to persuade him to resign.
Herschkowitz boycotted Habayit Hayehudi's coalition talks with the Likud at Ramat Gan's Kfar Hamaccabiah Hotel on Sunday night, to protest the pressure against him. He said he saw no point in negotiating with the Likud when matters needed to be resolved inside his own party.
Orlev and Orbach have threatened to vote against the government if Herschkowitz becomes a minister and does not quit the Knesset.
Herschkowitz has responded that he wouldn't join the coalition if the party split.
Herschkowitz met with Prime Minister-designate Binyamin Netanyahu at the Knesset on Monday, but neither side revealed whether progress had been made. Herschkowitz protested the Likud's putting talks with his party on the back burner during negotiations with Israel Beiteinu and Shas.
"There aren't any negotiations with us, unfortunately," Herschkowitz said on Tuesday when asked about the talks.
The sixth candidate on Habayit Hayehudi's list - Liora Minka, who heads the Emunah religious-Zionist women's organization - called for her party not to join the coalition if a minister for haredi education were appointed as Shas has requested.
"There cannot be two states for two peoples - one haredi and one not," Minka wrote in a letter to her faction members. "If two education ministers are appointed for two different sectors, it would prove that Israeli democracy has failed. Habayit Hayehudi should not join such a government."