[BroJoeK]

x on "the democracy": "People say it goes back to Andrew Jackson's era, or less often and more questionably to Thomas Jefferson's...
You can also check Google Ngrams."

Hmmmm… the Ngrams graph shows the term "the democracy" was used as much in 1800 as it is today, but does not tell us what it referred to then or now.

Wikipedia tells us "the democracy" referred to Jacksonian Democrats, but no details on when or why first used.

No other search I can think of produces more information.

Ah well...

[x]

There's an idea that the Jacksonians called themselves "the Democracy" because they wanted to be seen as a movement of the people, not just another political party. The name of the party officially became the Democratic Party in 1844, but it was still commonly called "the Democracy" until the Civil War, with the term revived in the 1870s and 1880s. William Jennings Bryan still referred to his party sometimes as "the Democracy," but the term became much less common by his day.

The 1912 platform refers to the party as "the Democracy" once, but that seems to be pretty much the end. There was plenty of talk of democracy in the Wilson years, but that is in other contexts, not as the name of a party. If that was the end it makes sense: voters in 1912 would still have had memories of the 1880s, 1870s and 1860s, when the term was more common. I suppose for young liberals in the Twenties the term would have sounded very old-fashioned - something they wanted to leave behind.