The Democratic Party was founded back in 1828. It was dominant in the Second Party System. But at the end of Reconstruction, it fizzled out. The Northern 'Bourbon Democrats' all joined the Liberal Republicans. Heck, the Southerners abandoned the party by the 20th century! So, could the Democrats have survived to the modern day at all? Or was their collapse an inevitability?
I think if they did, the Democrats would be ultra-conservative. I mean, look at how they felt during the Civil War and after. It'd probably be a regional party in the South, maybe the West too.