Netanyahu is under pressure to keep his coalition government intact. Two far-right partners have threatened to bolt in protest at any deal they deem to spare Hamas. A centrist partner, ex-general Benny Gantz, wants the deal considered. Hamas has provisionally welcomed the Biden initiative.
Opposition leader Lapid has indicated that he intends to support Netenyahu if his coalition falls apart due to the deal. Of course, such transactional support offers tend to be fical, and Netanyahu needs perpetual support in order to avoid jail on corruption charges.
Unfourtuantly, such a realignment (or, at least the threat of one) to a more centrist coalition is the only plausible path to a deal.