Why is it in the United State's national Interest to care what's happening between Israel and Palestine?
Israel is historically (after the switcheroo of 1960s alinements) America's beachhead in Middle East, in contrast to Soviet-client (these days Russia but no big difference) Arab states.
Why is America interested in Middle East? First, oil. Second, to prevent another hegemon (USSR/Russia; or regional like Turkey or Iran) from taking influence over the entire region and harnessing its resources.
If you're asking "What's the big deal", remember that Osama Bin Laden's main, and explicitly stated, beef with USA that led to 9/11 was basing US miliary in Saudi Arabia; and its relationship with Saudi rulers. As such, imagine if Israel isn't there. USA would have to have MUCH closer ties and explicit military relationships with other countries in Middle-East... so we get all sorts of local Osama's objecting to that to a higher degree than now.
Israel serves as a useful flashpoint for terrorism and Muslim anger. In case you forgot, USA's a "great Satan" and Israel is merely "little Satan". If Israel's gone, USA no longer has a flashpoint to deflect this, and becomes primary target.
Military industrial mutual symbiotism.
USA gets to have access to cutting edge Israeli military technology and research (see enhancements Israel demanded to Bradley for a very random example).
USA gets to field-test its military hardware in real combat situations
USA has a ready-made market for its military-industrial complex (a vast majority of money from USA's foreign aid, is gotten on a condition of spending that money right back in the States on military purchases).
- As a side effect of that, USA gets to enforce on Israeli's military industrial complext the right to veto ANY arms sales; which happens either when USA doesn't want some advanced technology being given to potential opponent; OR when that sale would constitute a competitive challenge to USA's sales).
This one's more in Geopolitics column, but USA has stockpiles of reserve hardware in Israel. In case of rapid theatre deployment needs, they don't need to worry about transporting that hardware across the globe, merely flying in personnel.
As I noted with references on another answer on this site; US Evangelicals (a super powerful demographics whose most recent leader was G.W. Bush) are strongly pro-Israel for theological reasons.
Another distinct pro-Israeli slice is moderate liberals who feel guilt over Holocaust.
Another somewhat distinct slice is non-Evangelical right-wing people who like Israel for being a democracy in an Middl-Eastern ocean of dictatorships or simply for being on - as they see it - Western Civilization's side in the conflict of civilizations (I'll leave aside whether that's a correct representation but the thinking definitely informs a sizable chunk of population).
In all fairness, this isn't "national interest" column, but it's a reality that a representative democracy like USA can not ignore no matter objective interests.