I've been doing some research recently and it seems quite apparent that the relationship between Israel and the USA wasn't as solid as it is today in the first couple of decades of Israel's existence. It seems that Truman's administration (if not Truman himself) and Eisenhower (Suez Crisis etc.) were far more sympathetic with the Arab cause than any recent President and particularly Lyndon Johnson. Is it fair to say that the relationship as we know it today has only really been this way since the war in 1967 or am I missing something?
Well, in part--the formation of the US-Israel alliance was a gradual process, but 1967 was a big year in it.
It began, ironically, by Israel not getting along with the US during the Suez Crisis. Egypt nationalized the Suez Canal, to the great anger of the UK and France. Backed by them, Israel invaded the Sinai. The USSR took the side of Egypt, and international pressure from the US forced the Israel/UK/France coalition to back down. The result was that Egypt became Soviet-aligned, which resulted in Israel becoming US-aligned, even though the cause of it was things not going nicely with the US.
Anyway, '67 was important because it showed that Israel could hold its own against the Soviet-backed Arab states. But it also showed the US that the Arab states were heavily Soviet-backed, which pushed things to more of an alliance. Importantly, in 1966 Israel managed to snag a MiG-21 (here is an article about it, they got an Iraqi fighter pilot fo defect) and handed it over to the US, which set the stage for post-67 alliance.
However, I might argue that '73 was more important. Unlike in '67, Israel didn't strike first after mobilization. Part of that was because the imminent attack was much less obvious (they were tipped off in '73, '67 had weeks of digging in), but the Israeli government asked the US about striking first, and they nixed it. And throughout the war, the US was able to use aid to pressure Israel to do its diplomatic bidding, by working towards cease-fires to prevent the conflict from escalating to involve the USSR. In short, Israel found it could get the aid it needed (Israel was a fairly poor country for much of its early history, and suffered a serious economic crisis in the '70s) by letting the US have some say in their foreign affairs and military actions, and the US found that by providing them with aid, they could both counter the Soviets and exert more influence on events in a conflict hotbed.
Another key event was the Israel-Egypt peace agreement in '79. It was brokered by the US, and included American aid to both parties, as a way to give the US a bit of leverage to make them keep the peace, which would keep war from reaching dangerous international escalation, as in '73.
You can see that in this table of American aid to Israel. Aid increased irregularly starting around 1966 (when Israel handed over that MiG), then increased more steadily in 1971, and really skyrocketed in 1974. It fluctuated in the 70s, but remained at a relatively constant high level after 1979.