According to Historian Mark E. Neely Jr. in his work, The Boundaries of Political Culture in the Civil War Era, politics were immensely important to 19th Century Americans. They were engaged with political culture in a way that seems alien to us today. This did not confine itself only to Presidential Election years. In fact, local and state elections were widely participated in at a level that rivaled Presidential Elections. An example he gives is that during the Gubernatorial Election in Pennsylvania in 1856, 85% of the enfranchised populace cast votes. That is a startling statistic by any measure, particularly when compared today with less than half the voting populace of the US voting in current Presidential Elections, much less local and state ones.

Historian Herbert Doherty in his work, The Whigs of Florida, argued that in fact local politics, platforms, and elections were more important to the populace than presidential ones. Local issues took precedence to voters, hence the survival of particular party affiliations, like the Whigs or No Nothings, long after their national party infrastructure and prospects collapsed.

Lastly, Neely Jr. argues that voting returns are not the only proof of this widespread engagement. The massive presence of party newspapers, material culture artifacts (badges, posters, lithographs, etc.) illustrate that the consumers drove a huge demand for politically affiliated consumable items, which were artist designed and commissioned, rather than politician driven.

So, as we can see, state and local politics were massively important to 19th Century Americans, who consumed political cultural items and took part in elections at every level in numbers that dwarf today's participation.

Why did it change? I'll let another scholar answer that, but it stems from the corruption and corresponding cynicism of the electorate that arose during the Gilded Age and Progressive Era.

Sources: Neely Jr, Mark E. The boundaries of American political culture in the Civil War era. Univ of North Carolina Press, 2005; Doherty Jr, Herbert J. "Florida and the Crisis of 1850." The Journal of Southern History (1953): 32-47; Doherty Jr, Herbert, The Whigs of Florida 1845-1854, Gainesville: University of Florida, 1959.

Trivia: Thomas Jefferson actually left off his tombstone that he was the president of the United States. He put some of his other accomplishments instead.