Israel is a hot button issue in the US, and there are many interest groups that have strong feelings about it. For sure, domestic pressure plays a role in US-Israel relations, and that's an important part of the picture.
So while there are domestic reasons why the US supports Israel, Israel is in fact somewhat peripheral to the US' strategic interests in the Middle East. The core of the US strategic interest in the Middle East is in promoting stability of Arab states, ensuring the free flow of oil out of the region, nuclear non-proliferation, and countering terrorism. Iran's interests are often is directly at odds with those interests of the US, and it has nothing to do with Israel: it has to do with the complexities of the state system in the region (most especially, that Arab states are collapsing because they are weak and incapable of securing a monopoly of power within their own borders, and Iran is taking advantage of the weakness to project its power). In fact, there are often times when US strategic interests conflict with Israeli interests and the US has no problem going over Israel's head (see, for example, the JCPOA), and when the US sees the US-Israel relation as a liability (you might recall some remarks that Mattis made years ago, when he said that the failure to secure a peace deal between Israel and the Palestinians made it more difficult for the US to build coalitions in the Middle East -- a prevalent view for a number of years. But there are examples of this, especially if you go back in time. They range from bin Laden citing US support for Israel as a motivation for 9/11 to Eisenhower in the 1950s believing that close ties with Israel would be an obstacle to US relations with Arab states).
It goes without saying that it's all complicated. Regarding Israel and KSA's influence on US policy towards Iran specifically, certainly Israel and KSA were both on the same side when it came to the JCPOA. Both lobbied the Obama administration and the Trump administration (and, in the case of the Obama administration, neither was able to leverage their power into getting what they wanted), and there's some evidence that they've even acted in concert.
I don't know who's to say which one of KSA or Israel has more influence on US foreign policy than the other in general, or how you'd measure it. There isn't a simple answer, and it's also something that's changed over time and has varied from president to president. The US primarily fought the first Gulf War because it was worried that Iraq would invade Saudi Arabia, and it could not under any circumstances permit the fall of KSA. (Meanwhile, president Bush 41 insisted that the Israel not defend itself during the war, even though Hussein threatened to shoot chemical warheads at Tel Aviv. That whole episode was humiliating for Israel and made the country feel deeply vulnerable, which contributed to Israel feeling that it was imperative to come to an arrangement with the Palestinians. Oslo followed.) Back in the 2000s, during the early days of the Bush 43 administration, KSA threatened to radically change its relationship with the US because it didn't like how Israel was handling itself during the second intifada. In response, Bush promised KSA that it would officially endorse the view that a Palestinian state should be founded -- something the US hadn't formally done before. So there you go: it was a very different time than today, but there's an example where KSA was actually able to dictate to the US what it should do regarding Israel.
KSA used to have much more leverage over the US than it does now, now that the US is a net oil exporter, and, in fact, the same is true of Israel, now that the Cold War is over and the US no longer uses its alliances with Egypt, Turkey and Israel to keep Russia out of the region (in fact, Russia's back in, and its cozying up to both Turkey and Egypt, but especially Egypt). Despite whatever pro-Israel gestures Trump has made regarding Israel during his administration (many of them, very likely, done primarily for domestic political gain rather than any kind of strategic purpose, and not in such a way as to promote Israel’s own strategic goals, even as it understands them), there's also a strong isolationist bent to his foreign policy that is really an extension of the Obama foreign policy, and it's hard to imagine an American president being elected who advocates more intervention in the region. The US wants to get out, and so Israel is becoming less important (and so is KSA, which has something to do with why the two countries are becoming closer: they're trying to use their collective leverage, not only to convince to the US to take a more active stance in combatting Iran, but even just to keep the US engaged in the Middle East at all).
Anyway, Israel's becoming less important in US foreign policy, and it has less leverage over the US than it once did. (Furthermore, Israel is increasingly becoming a polarized issue in domestic politics in the US, and support for it is no longer as firmly bipartisan as it once was. Even the Jewish community is becoming more much divided in its support for Israel, a trend that began to pick up steam under Obama but is accelerating even faster under Trump. The most consistent support for Israel comes from evangelicals, and even that's slipping.) The smart money is on the idea that the US-Israeli relationship probably peaked during the 90s or the 2000s (there are reasons why Israel is trying to develop strong bilateral relations with Russia, India and China. It's a hedge not only against the decline of the US-Israeli relationship, but also against the decline of US power more broadly).
