The terminology is, well, wrong. That's because the terminology has been hijacked.
The question should be, "When did the United States become majority
Progressive?"
"Liberal" in its original meaning meant "In favor of individual liberty," and the nation started out on that footing (please spare me the "so long as you were a White Christian male" rhetoric - historical perspective, people.)
Marx's Communist Manifesto was published in 1848, and had made its way around the intellectual world by the late 19th century. It strongly influenced the movers and shakers in Europe and here, and is largely responsible for the burst of "Progressive" amendments to the Constitution that took place in the very early 20th Century - Income tax, February 1913; Direct election of Senators, May 1913; Prohibition, January 1920; and Women's Suffrage, August 1920.
The election of Woodrow Wilson in 1913 corresponded to the rise of Progressivism - and illustrated that Progressivism is
anything but "liberal."
Once the majority of the public understood this, the Left dropped the "Progressive" label and suborned "liberal" as their own. Now that we grasp that "liberal" isn't, they're switching back to "Progressive."
It's been a long, slow crunch since then - what
italian Communist Antonio Gramsci termed "the long march through the institutions" - education, media, politics.
When was I sure that Progressivism had become dominant?
When Barack Obama got RE-elected.