Of all the large Jewish communities in the modern world, that of the United States has probably sent fewer immigrants to Israel than any other. If you know where to look - Katamon, say, or Har-Nof in Jerusalem, or Ra'anana - they are quite visible, and in some professions they simply can't be overlooked. Reform rabbis, for example. But in large swathes of Israel they're quite thin on the ground. All Israelis have been in America, more or less, but Israel's Jews are not American Jews. Different agendas, different worldviews, different sentiments.
In the political sphere, there have been more Americans than many people realize, especially if you count Canadians such as Dov Josef. Two, however, stick out. There was the one who served as prime minister in the early 1970s. And there was Abba Eban, who actually never held American citizenship but stood out from a mile away for being as un-sabra as they make them, and whose English was easily better than that of any run-of-the-mill Oxford don.
Martin Kramer (an American who lives in Israel) tells the oddly touching story about how Eban magnificently represented Israel in America for its full first decade, and then, when the time came to go home, was informed he wasn't an Israeli at all.