Democrats didnt start the Civil War, the South did. Support for secession was regional, not partisan. In fact, in the South some of the biggest support for secession came from Whig regions. Similarly, unionism in the North was sectional and not partisan, with Democrats supporting it as well as Republicans.
In our era it seems to be Republicans who are drifting more towards civil war, or at least abandonment of democracy. Like the antebellum South, modern Republicans realize that they cannot win majority support from the people and so are relying on undemocratic rules to maintain power. Theres also more talk of resorts to extreme measures if they do ever lose power