I would highly recommend reading Last Call by Daniel Okrent. The short version was that it was a coalition of labor, suffragettes, and pro-temperance types. They each had their motives, and there was a lot of political horse trading as well. There were some rather adroit moves as well -- certain exceptions were carved out in order to keep certain constituencies happy. For example, farmers were allowed to "preserve" a certain amount of their fruits (which meant fermentation). Religious production and use of wine was still allowed (to keep the Catholic vote somewhat pacified).

There was a lot of proselytizing of the cause. Gough (who had a street in San Francisco named after him, which I find very funny because San Francisco loves booze) gave somewhere close to 10,000 speeches. PT Barnum was in favor of it. William Jennings Bryan was in favor of prohibition and even served grape juice instead of booze when he was secretary of state.

Wayne Wheeler was one of the main brokers though. A critic once said that he "controlled six congresses, dictated to two presidents [and] held the balance of power in both Republican and Democratic parties."

You are right, however, to think that it was opposed. Representative Richard Hobson introduced it in the house and the Speaker remarked that Hobson was a lunatic. Prohibition never polled well. It just navigated the process expertly and with lots of deal making.

The first half or so of Last Call covers this at much greater depth than I can in just a single comment here.