As with most things American Jewish history related, the origin of it is in the late 18th and early 19th century. It was a time of massive change in the American Jewish community. The population, which was composed mostly of Sefardi (Spanish) and German Jews, expanded massively with immigrants from Eastern Europe, triggered by successive waves of pogroms, beginning in 1881.

Anyway, these immigrants were mostly urban, and mostly lower-class. As a consequence, they were involved in the labor and socialist movements. The best known Yiddish newspaper, The Forward, started out as a socialist paper. The Workermen's Circle was a socialist organization, too. And the distinctly Jewish political movement of the era (besides Zionism) was Bundism, which was expressly socialist.

So, Jews were big into socialism. Over time, this lead to their inclusion in the New Deal coalition, which lead to a strong Democrat lean. This has the Jewish voting patterns in presidential elections from 1916 onwards. Note that socialist Eugene V. Debs, running from prison in 1920, who recieved 3.4% of the popular vote nationally, got a whopping 38% of the Jewish vote. And from Al Smith in 1928 after, no Democratic presidential candidate got less than 60% of the Jewish vote except for Carter in 1980.

As for before that occurred, I can't find any solid data. This article says that the Jews prior to the New Deal coalition were mostly Republican. But the definite association with progressive politics is a labor movement/socialist/New Deal phenomenon.