When talking about the history of environmentalism in the United States, it is important to realize that some of those ideas are relatively older, but were considered conservationism. Conservationism is a slightly different notion (preserving environmental landscapes or organisms, etc., for future generations to use — e.g., save the bison, so future generations can hunt the bison), but it does introduce some of the notions of human impact, lost "nature" (a complicated construct), and sets up something of a dichotomy of use versus "saving." Think Henry Thoreau and Teddy Roosevelt.

The transition from that to environmentalism in the early 1960s has a somewhat interesting trajectory. There was a definite impact from the nuclear fallout debate prior to the Limited Test Ban Treaty (1963). This introduced, in a new way, the idea that remote, relatively localized operations could have massive environmental effects throughout an entire ecosystem. When you set off a nuclear weapon in the desert of Nevada, the radioactivity can be traced through the ecosystems of the entire country (sometimes even the world) and back into human bodies (quite literally — baby teeth proved to be a potent way to show how fission products from nuclear tests got into human bodies, via the calcium-like strontium-90 isotope) — radioactivity is much easier to detect than chemical contamination (with a Geiger counter, you can literally track individual atoms of radioactive substances, whereas you are really limited to various parts per million for chemicals), and a whole lot of ecological research came out of this field (funded by a Cold War infrastructure that was both eager to reassure the public that these tests were safe and necessary, as well as by anti-nuclear people who wanted the testing to slow down or go away). Politically it was one of the major public health and security debates of the day, and was extremely high-profile.

It is not long after that you get Rachel Carson and the Silent Spring book (and debate). Carson herself used the fallout debate as an analogy to what she wanted to talk about, which was pesticides — again, a trace chemical that enters the ecosystem and food chain and potentially disrupts it violently. There are two really interesting angles of Silent Spring, the "we are destroying the environment" side of things (killing eagles, killing nature, making the spring go "silent", etc.) and the "we are poisoning ourselves" side of things (pesticides and pollution as essentially an uncontrolled experiment on human beings of fantastical proportions). Carson's allegations were taken up at extremely high levels, up to the President's Scientific Advisory Committee (PSAC). Kennedy himself commented on them, and convened further studies as to whether the American chemical industry was essentially poisoning the nation. While there were some strong denials of Carson's claims (notably by said industry) there was enough to them that there was serious discussion and consideration about at least the self-regulation of emissions of various sorts (in those pre-EPA days).

The Space Race, and the photos of the Earth from space, also have been claimed to play a role in this new emergence of a sensibility of the planet as a very bounded, limited resources — a "spaceship Earth" (as Buckminster Fuller liked to call it), a "pale blue dot" (Carl Sagan), a fragile, interconnected island whose ecosystem has definite tolerances, whose animals have definite limits (the idea of extinction is much older of course, and this is where the conservationism comes in), and even a moral component about non-intervention and preservation-for-its-own-sake (not quite conservationism) that emerges.

These things have always been controversial but reached enough of a consensus that no less than Richard Nixon could sign a law to create the Environmental Protection Agency by the end of this "cycle," and the notion of environmentalism, the harmful effects of pollution, the detrimental blight of the despoiling of nature, and the hazards of endless, heedless growth became pretty standard parts of the American lexicon by the 1970s, well outside the circles of conservationists, hippies, etc.

Like all complex social movements, pin-pointing it to a single event is difficult, and often even where you can pin-point something (say, Carson's Silent Spring) you end up in a somewhat recursive situation (asking "why did Silent Spring make such an impact?" moves you up to previous conditions that "prepared the field" and so on). I don't think anything above is controversial in discussing this history, though, but one can probably find other factors to highlight. Short version of this is that it didn't quite "suddenly take off," that it was a bit more gradual than that, and some of these ideas were relatively old (i.e. conservationism) but got recombined in new ways with new issues of the day. The historian of technology Paul Edwards, for example, in his book on Cold War computing (The Closed World) would probably also note that the idea of a "Green World" is in some very interesting ways the direct counterpart and antithesis to the hyper-controlled technoscience notion of the Closed World enabled by computing; in a sort of Hegelian sense, the ascent of one gives birth to the other.

There is a rather large literature on the history of the environmentalism movement. The work of William Cronon on the construction of "nature" is a very good starting point. For details on Carson, fallout, PSAC, Kennedy, etc., see esp. Zuoyue Wang's In Sputnik's Shadow which has a very nice chapter on this. There is also a very nice article on JSTOR on the fallout-Silent Spring connection (R.H. Lutts, "Chemical fallout: Rachel Carson's Silent Spring, radioactive fallout and the environmental movement," Environmental Review, 1985). There is also a big literature on the cultural impact of "earthrise" photos — I get my thinking on this largely from the work of Sheila Jasanoff but there are many others who have written on this.