People missing the point ITT.
No, Israel doesn't directly rely on oil money but indirectly they do because the US gives two shits about Israel for a couple of reasons: 1) Holocaust Guilt and 2) Israel is a useful (de)stabilising influence over Middle East countries thatdohave oil. Oncetheiroil runs out (and once the Holocaust is out of living memory), Americans are eventually going to start asking questions along the lines of "Wait, why should we we give any fucks about them?". If Israel hasn't come to some sort of arrangement with their neighbours by that point, it might get...messy.
tl;dr - Israel will eventually stop being useful in a realpolitik sense. Once they do, the American support and money will also stop at some point and, well, it's generally considered better to negotiate from a position of strength rather than weakness.