In the past few days, after the sixth Israeli strike on a Gaza UN shelter for Palestinians fleeing the fighting, the Obama administration sent some pretty harsh words Israel's way. The attack on the UN facility in Rafah was "indefensible," according to Senior Adviser to the President Valerie Jarrett, who added that you "can't condone the killing of all of these innocent children." UN Ambassador Samantha Power called the Rafah strike "horrifying;" a longer State Department statement named it "disgraceful."
It's hard to imagine a clearer signal of administration outrage with Israel at the Gaza campaign, short of a personal statement from the president. The US is clearly upset with Israel, which isn't all that rare, but this level of public criticism is very unusual. Given the US's strong commitment to supporting Israel, the Obama criticism probably does not augur any substantive change in that pro-Israel US foreign policy. But it could still matter by impacting domestic Israeli politics, which are highly sensitive to fears of "losing" American support.
American policies toward Israel likely won't change much
As harsh as the administration's language has been in the past few days, it's hardly been backed up by any meaningful public action pressuring Israel. On July 31st, for instance, the US agreed to an Israeli request to resupply its grenade and mortar round stockpiles. There's zero indication that the US is going to take tangible steps to punish Israel, either by limiting defense cooperation or letting through a UN Security Council resolution condemning Israel's conduct in the Gaza war.
This isn't very surprising. For strategic and political reasons, the United States will likely maintain its policy of remaining very, very close to Israel for the foreseeable future. America's deep commitment to the US-Israel relationship means America's leverage over Israel is pretty limited. It usually applies what pressure it can bring to bear in cases where direct American interests are at stake — keeping Israel out of the Gulf War, for instance, or limiting Israeli arms deals with China. That's not perceived to be the case in Gaza.
This sort of public criticism, then, isn't the beginning of a major Obama attempt to change US foreign policy toward Israel over Gaza. In a very immediate sense, the criticism is exactly what it looks like: the Obama administration is upset about Israel hitting a UN facility, and wants to publicly condemn the events.
Still, the statements could have a real impact within Israel
Israelis value their relationship with the United States — for fairly obvious reasons. The main concrete way that harsh US criticism of Israeli conduct could matter, absent any more material American actions, is by leading Israelis to believe that their government is endangering their relationship with the American president and the United States.
Netanyahu is usually seen as the poster child for this theory. Netanyahu is his country's Grover Cleveland: he was defeated after his first premiership in 1999, and only won a second term later, after several years out of the prime minister's office. There's a theory that his 1999 defeat was a result, at least in part, of his super-tense relationship with the Clinton administration, during which Netanyahu resisted American pressure. Israeli voters panicked over Netanyahu's very public spats with Clinton over the peace process, and elected Ehud Barak, whose views on the peace process meshed better with Clinton's.
This theory is not perfect. For one thing, Clinton had all but endorsed Netanyahu's rival Shimon Peres earlier, in 1996 — and Netanyahu won then. And in 1999, a plurality of Israelis prioritized domestic issues over foreign affairs in pre-election polling. "In 1999 there were more immediate reasons for his defeat than the lack of rapport between Jerusalem and Washington," Ha'aretz writer Anshel Pfeffer wrote in September 2012, before the 2013 Israeli elections. In other, the US wasn't the decisive issue.
"But 2012 is very different," Pfeffer wrote. "Surveys show that Israelis are more concerned over losing their strategic alliance with the United States than they fear an Iranian nuclear bomb." Netanyahu lost ground in the January 2013 elections just after Obama — with whom the Israeli premier has a famously poor relationship — was reelected in November 2012.
But Netanyahu only lost seats in the Knesset; he didn't lose his job. And once again, it's not obvious that US-Israel relations were a cause, let alone a principal one, of Netanyahu's setback. The bottom line, though, is that there's at least some evidence that publicly poor US-Israel relationships can make political headaches for Netanyahu, which is a real if indirect form of pressure — even if the US won't actually punish him over Gaza.