I lean towards Jackson starting the Democrat Party, with the old Democrat Republican Party fading away (somewhat rebranding itself into a new party, but not officially) and some of those members becoming the National Republican Party. That didn't go much anywhere, and those folks became the Whigs. Which also didn't last long, and the remaining folks became the Republican Party we know today (including a Whig named Abraham Lincoln).
A Jefferson–Jackson Dinner is a title traditionally given to an annual fundraising celebration held by Democratic Party organizations in the United States.[1] It is named for Presidents Thomas Jefferson and Andrew Jackson, which the party traditionally calls its founders. They are usually held in February or March at a local level providing an opportunity for elected officials, candidates, party staff, advisors, and donors to attend.https://www.c-span.org/program/campaign-2008/indiana-jefferson-jackson-dinner/189225Due to controversies over Jefferson's slaveholding and Jackson's policy toward Native Americans while in office, some Democratic Party organizations have been removing Jefferson and Jackson from the title of party fundraisers.[3]
https://en.wikipedia.org/wiki/Jefferson%E2%80%93Jackson_Dinner
May 4, 2008
Campaign 2008
You can't make this kind of thing up. Â A one or two decades ago they were proud to say they were founded by Jefferson and Jackson.