48 hours
The quote is from a member of the Kahane youth, an Israeli extremist movement, interviewed in Haaretz. Not all members are as strong in their views. Some want to give the Palestinians a chance:
"[I]f we don't deal with the Arabs now, they will liquidate us and take over our country democratically. They will change our flag and our national anthem." He adds that he is not in favor of killing; he espouses expulsion of the enemy. They have to be given a 48-hour ultimatum to leave the country, "and whoever refuses, we will shoot him".
I find it helpful to mentally substitute "Jew" for "Arab" to better appreciate this sort of talk. Actually, it takes little effort to find historical counterparts for these kind of nationalist-racist groups of which Kahane Youth is but one (and not even the most extreme), with their emphasis on the sacred connection of the People and the Land, pornographical propaganda about "cannibalism in Gaza", adoption of ancient Jewish heroes as the movement's precursors, and so on. Members of the Kahane Youth evidently believe their views to be widely shared:
"I think my parents also think this way - it is pretty clear that they think like this - and in fact almost the whole people of Israel thinks like this."
[...]
"Mom knows I am a Kahanist and she doesn't want it, she's afraid I'll be arrested, but she's happy that I am saying what I think out loud. Everyone has the same opinions. In their hearts every Jew knows that one Jew is worth more than five million Arabs and Jewish blood is sacred, it says so in the Torah."
In fact, such genocidal views are not part of the Israeli mainstream. Anti-Arab racism, demonisation of Palestinians, calls for massacres and ethnic cleansing are common fare (some parties in the government openly advocate ethnic cleansing), but explicit demands for the physical extermination of all Palestinians are some way beyond mainstream sentiments.
However, such extremism could not thrive if it didn't reflect something in the popular consciousness. Indeed, in Israeli mainstream discourse it is perfectly respectable to consider Palestinian children to be a threat by virtue of being born. (Here's a typical example of a reasoned view on the "demographic problem". Again, it is an interesting exercise to mentally substitute "Jew" for "Arab" while reading.)
The perception of the Kahane Youth that they're just saying out loud what everyone silently believes reminds me of skinheads in Finland. The basis of skinhead ideology is also not that different from prevalent prejudices, and their views also say something about Finland. Why would the young be ashamed to say in public what the parents are thinking in private?