How does the level of political polarization in the U.S. today compare to the years just prior to the Civil War?

This is probably more of a question for /r/Ask_Politics, but I can give you a basic reason why this is so difficult for anyone to answer.

The attempt to compare political polarization to pre-Civil War polarization is very, very difficult not only because of the shifting parties, but because of the alterations in culture. For example, today we allow parties like African-Americans and women to vote, whereas before the Civil War we did not. The alterations in the political landscape could conceivably have led to party polarization as parties hoped to move towards things like affirmative action (or against it) in order to better establish a base among the other voting groups that are no longer just "white males" (simplifying, here).

The other problem is the question of "How do we measure polarization?" Is it based on how often one votes a party line? Is it based on how many laws get passed vs. filibustered + defeated because compromise couldn't be reached? How accessible are the records on all that, if that's the method, and how are we to measure them in the fluctuating parties as the Republicans and Whigs existed? Also, how does polarization get affected by voter turnout and mass communication changes since then: are we accurately measuring the polarization of everyone, or just the politicians?

Also, how do we know whether or not polarization has occurred among the general populace, or if we've simply self-sorted to live among people who are like-minded (as some argue California has over the past 3 decades, for example) and thereby contributed to politician polarization without public polarization? Or, in that self-sorting, did we fall prey to the group polarization effect?

It's a difficult question to answer, and it's not one I can give you an answer to. I don't feel qualified, and I don't know any studies on the subject to suggest (most I've seen relate to California, which I learned about, and only about the recent decades), but I hopefully can help clear up why this is so difficult to understand and why you may not get an answer.

Good luck!