Eventually...
I think the period was one of idealism in politics. The American revolution, the French revolution, the Jacobin uprisings in the UK (Tolpuddle, Peterloo), even the start of communism (I think I remember Marx writing his famously misunderstood book about this time...). I think everyone seemed to have just got bored of monarchy all at the same timeI agree that I don't think you will get the same idealism now.
I think Europe's problems at the moment is that they are not states as the American states are/were but countries that are far more different and older and stubborn. Most of whom have ruled over most of the others at some point or other. The UKs alliance with France, for example, is very recent and we have been at war with them far longer than we have ever been at peace. So we'll never get that unity, at least not for a long while.