In 2005, relative moderates within Likud, led by Ariel Sharon, split off from the party and established Kadima, a center-right party that was somewhat less hawkish and open to reaching a peace deal. The party won the 2006 elections, and was also the largest single party in 2009, albeit in the opposition.
Kadima is basically dead now, a minor party of two seats likely to miss the threshold in the next election, but Israeli polls are showing strong support for the basic idea behind its creation, and show a majority would vote for a hypothetical Benjamin Netanyahu Party created along the same lines.
Though back in 2005 Netanyahu was seen as part of the “extreme right” of Likud that Kadima was getting away from, in 2014 he is seen as a comparative moderate in the party, willing to at least theoretically negotiate with the Palestinians at a time when many of the party’s hawks are rejecting talks on general principle.
Netanyahu has recently clashed with the Likud leadership, which has sought to kill the talks, and while Netanyahu is still far from a “pro-peace” candidate, within Israeli politics his comparative lack of venom for all things Arab makes him positively dovish.
It’s unclear where the dividing line is between the “soft right” of Netanyahu and the sociopathic far-right within Likud, but the poll suggests that among Hebrew-speakers, Likud’s strongest constituency, the support would go to Netanyahu if a split happened, and it might even make his party more appealing to centrists averse to Likud’s fringe-right members.