But not the way you see it, just the opposite:
After ratification in 1788, Jefferson took charge of the anti-Federalists' who opposed the Constitution, becoming the anti-Administration faction and, in time, the Jeffersonian Democratic Republicans.
Jeffersonians were supposedly the party of the "little guy", the yeoman farmer (then over 80% of voters), as opposed to Big City Federalists, but over time the reality became quite different, when Jeffersonians took over Washington DC after 1800 and never let go.
In time, pro-Constitution Federalists faded & collapsed in Northeastern cities (the kill-shot was their discussion of secession at the 1814 Hartford Convention) and Southern Jeffersonians became Jackson Democrats -- the alliance of Southern slave-holders (i.e., Calhoun) with Northern (i.e., van Buren) Big-City immigrant bosses.
This anti-Constitution alliance held until circa the 1960s when the descendants of slave-holders were replaced by descendants of slaves as the Southern Democrat base.
Meanwhile, the old pro-Constitution Hamiltonian Northern Federalists, driven out of cities, reformed as rural-based Whigs and, with the addition of anti-slavery ideas, became 1850s era Lincoln Republicans.
By the 20th century, progressives had taken over the old Jeffersonian Democrats, making them also the party of Wilson, Roosevelt & LBJ, of all-powerful Federal Government and, yes, war.
1840 Presidential election by county.
Brown is Whig Harrison, blue Democrat van Buren.
Note Democrats have already taken over Northern big-cities while Southern Whigs are strongest in areas that remained Unionist during the Civil War.
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So: Jeffersonian Democrats were the anti-Constitution party of Big-city immigrants, slavery and all-powerful Federal Government.
Pro-Constitution Hamiltonian Federalists became the party of rural, small-town & suburban, smaller-government, small-business, farmers, anti-slavery, Christians & traditional Americans.
In the rush of Jeffersonian Democrats to internationalize our population and globalize our economy, the old Hamiltonian Federalists are Trump's "forgotten people", famously, in Obama's words, "bitter clingers" to guns & religion, in Hillary's words, "deplorable & irredeemable".
So, when today's Jeffersonian Democrats tell us "you're not who we are", the "you" they're talking about are Americans who still value our history and traditional heritages.