There was no sign of a breakthrough in talks with the far-right former defense minister, Avigdor Lieberman. Parliament began a full-day debate on a motion to dissolve itself and call a new election if no deal is struck.
Political sources said Netanyahu was seeking agreement with the leaders of parties in the legislature for a mid-September election day.
Netanyahu had declared himself the winner of a national ballot last month, but he now has until midnight local time to tell President Reuven Rivlin whether he has put together an administration, and his political future hangs in the balance.
Failure to forge a coalition would take the task out of the 69-year-old Netanyahu's hands, with Rivlin asking another legislator, either from the prime minister's right-wing Likud party or from the opposition, to try.
That presidential move, can be avoided with a coalition agreement deal or if parliament approves an election.
Political commentator Chemi Shalev, writing in the Haaretz daily, said a last-minute agreement was still possible and Netanyahu would still be the favorite to win a new poll.
But he said Netanyahu's critics now find themselves fantasizing about a world without him.
"It's not an easy task, given his decade in power and the four more years he supposedly had coming. Young Israelis can't even begin to imagine an Israel without him: Netanyahu as prime minister is all they've ever known," Shalev wrote.
Without the support of Lieberman's Yisrael Beiteinu party, which has five seats in the 120-member Knesset, Netanyahu cannot put together a majority government of right-wing and religious factions led by Likud.
Political commentators said that as the prospects dimmed for a compromise with Lieberman, Netanyahu would focus his efforts on enlisting the 61 votes needed in parliament to approve a new election.
Lieberman said on Wednesday he was not backing down in what he termed a matter of principle over the conscription issue. He also denied allegations from the Likud party accusing him of attempting to oust Netanyahu and lead a "national camp."
"I am not a vengeful man and I don't hold a grudge," said Lieberman, who last year resigned as defense chief in a dispute with Netanyahu over policy toward Gaza.
Stakes are high for Netanyahu who is facing possible indictment for three corruption cases. Netanyahu is allegedly looking for legislation in the new parliament that would give him immunity from prosecution. New elections might make it impossible.