Progressivism also got some business support because the alternative seemed to be someone like William Jennings Bryan. The ambivalent relationship between government and business was exemplified by that between Theodore Roosevelt and J.P. Morgan. Morgan supported Roosevelt's reelection because he knew Roosevelt would win, not because he was happy the president had launched an antitrust suit against Morgan's Northern Trust. And when the two men cooperated, as in the Panic of 1907, which I recently wrote about, it was because they felt they had to, despite their differences.
UPDATE 1/12: More thoughts above.