A reader ("nycerbarb") sent me to this fine article by one Rabbi Jill Jacobs. Jacobs tells the history of the Tikkun Olam idea from its earliest appearance in Second Temple times - i.e, post-Biblical - and shows how it has meant different things at different times. She is unabashed in saying the present term stands for an American ideal, first used in the 1950s. She likes this usage, and shows that the four main earlier meanings can, if you wish, be understood as contributing to the present one.
Her history is fine, so far as I can judge. Her reasoning is, well, reasonable. A bit contrived at times, for my taste, but most peoples' reasoning is a bit contrived from time to time. Having Googled a bit I get the feeling Rabbi Jacobs and I might not agree on some things, including some rather important things, but I have real respect for her ability to make her case from a position of serious learning and knowing.
Then there's the matter of universality. American Jews - like European Jews a century earlier - are into it. They'd like to do things that may make the world fixed. Some of the prophets looked forward to the world one day being all fixed, and their formulations count as the most rousing ever, though their avenue to perfection ran along a religious path quite different from their modern disciples'. Since then, however, Jews have mostly concentrated on the same things other people focused on: doing their best in the world they lived in. Sometime in the 18th century some Jews began setting aside the communal and national frameworks (the prophets had never done that) so as to focus mainly on the universal. Moses Mendelsohn was an early proponent, Rosa Luxemburg was an extreme one, and Leon (Bronstein) Trotsky was an extreme example of how wishing to force the matter leads to mass death.
Still, for all the examples we'd prefer to forget, American Jewry can be said, by in large, to be informed by a version of this impetus, this wish to fix the world; nor is there anything intrinsically wrong with it. Israel is informed by a different vision, the one that recognized in the late 19th century that new world orders were all well and fine but the Jews wouldn't be allowed to fit into them, or in the case of the early socialist Zionists, the Jews might be allowed, but only if they came to the table as a viable nation, like everybody else.
As a committed Zionist myself, I can see that both visions of society have roots in Jewish history and thought; it seems to me that the one that aims at the Jews being actors in history is more compelling than the one that would have history become something else. This seems to me closer to the essence of Judaism, but also to the reality of the human condition. Jill Jacobs might think otherwise, and we could have a good argument about it - nothing is more Jewish than that, after all.