Jewish Home is expected to win from 14 to 17 parliamentary seats in Tuesday's election, McClatchy Newspapers reported. Seven to 10 of those seats would be losses for Netanyahu's governing coalition.
Netanyahu formed a coalition government after his Likud Party won 27 seats to 28 for the Kadima Party. The coalition included Yisrael Beitenu, which merged with Likud last year, the Labor Party and Jewish Home.
Chava Mizrachi, who has voted for Netanyahu in the past, told McClatchy he appears to have become "complacent." She said she might vote for Bennett.
"He's fresh and not from the corrupted old political system," she said. "I think his appeal is that he seems like a modern-day success story."
Bennett, whose parents emigrated to Israel from California after the Six-Day War, was born in Haifa. He served in the Israeli military, made a fortune developing anti-fraud software and entered politics as an aide to Netanyahu, serving as his chief of staff from 2006 to 2008.
After resigning from Likud, Bennett joined Jewish Home and was elected party leader last year. He supports Israeli settlement on the West Bank.
Netanyahu's government has become more intransigent on the settlements, under pressure from Jewish Home. One member of the Cabinet recently called for Israel to begin annexing pieces of the West Bank, while one Likud parliamentary candidate suggesting offering Palestinians $500,000 to move elsewhere.