Yes! While secession (the allegedly legal process by which a state could voluntarily separate itself from the Union) was not always the exact mechanism in play, the idea of 'disunion' was consistently invoked pretty much from the moment the Constitution went into effect. Elizabeth Varon wrote a wonderful book about this, called Disunion! The Coming of the American Civil War, 1789-1859, and argues

"'disunion' was once the most provocative and potent word in the political vocabulary of Americans...[it] conjured up the most profound anxieties of Americans as they considered the fate of their republic. This one word contained, and stimulated, their fears of extreme political factionalism, tyranny, regionalism, economic decline, foreign intervention, class conflict, gender disorder, racial strife, widespread violence and anarchy, and civil war..."

Basically, the nation was young and fragile in the eyes of most Americans. The idea that some threat, internal or external, could dismantle it was connected to myriad fears about missteps, disagreements, or disunity that could destabilize the Founding Fathers' creation. As Varon describes it, disunion rhetoric took several forms:

• Disunion as Prophecy: If a certain course of action is taken, the nation will be brought to ruin!
• Disunion as Threat: Do what we want or we will leave the Union!
• Accusation: By doing X, you will drive the Union apart!
• Process: The nation is headed for disunion unless X corrective action is taken.
• Program: intentionally taking actions to dismantle the Union (unifying the South and calling for secession falls under this category)

Disunion was a steady presence in the political discourse, whether or not the people invoking it actually meant what they said. Some examples:

• The Hartford Convention (1815), when a group of Northern Federalists gathered to discuss constitutional grievances and their opposition to the War of 1812. This was the culmination of years' worth of discussions about whether New England states should secede from the Union, or else expel western states (neither proposal had significant support at the convention).
• During the Missouri Compromise debates in 1819, many southern politicians invoked the Hartford Convention to try and paint their Northern opponents as disunionist.
• Throughout the period, it was common for southerners to claim that Northern antislavery sentiments were unwittingly disunionist, since they would allegedly foment slave revolts that would destroy the nation.
• Northern politicians protested the annexation of Texas by claiming it would destabilize political balance in the country and drive the North out.
• From the late 1840s, disunion was a major difference between antislavery Free Soilers and abolitionists, since the latter were often willing (in theory) to break apart the Union in order to end slavery.
• The Nullification Crisis, of course, had South Carolina threatening to secede if the federal government tried to enforce a tariff. John C. Calhoun's writings on the constitutionality of nullification and secession are well worth the read, despite his support for slavery.

Many more examples exist, but the point is that the spectre of disunion, however it was used, was a regular presence in American political discussions such that some came to view it as an idle threat. By the time a real secession attempt was mounted in 1860, it was possible at first to dismiss it as yet more empty rhetoric.