The Underground Railroad wasn't so much a threat to national harmony as to the artificial compromises that had been carefully cobbled together over a number of years between North and South. The truth was that no one in the American political class was really willing or able to confront the problems of slavery head on. Instead, they came up with ever more ingenious ways of avoiding taking the necessary hard decisions, while at the same time congratulating themselves on keeping the Union together.
The existence of the Underground Railroad, however, was a timely reminder that the issue of slavery wasn't just political, but moral. Whatever compromises may have been reached among politicians were completely irrelevant to those slaves willing to risk their necks by embarking on their dangerous, clandestine journeys to freedom. So long as they were prepared to do this, no one could feel secure that harmony between North and South, such as it was, would prevail forever.
The Underground Railroad ought to have alerted the political classes to the fact that slavery was a running sore in American politics that needed to be properly dealt with. But because the overriding consensus, North and South, was to maintain some degree of harmony, however artificial, this never happened, with tragic consequences for the nation.