The revolutions in Europe had a lot of variation to them but I can speak a little to how Americans reacted to Hungary's attempt to escape the Austro-Hungarian Empire. In short: Americans loved it but not enough to do much of anything about it.
A bit of context: the U.S. was viewed, by Americans and many Europeans, as the first modern implementation of republican government and were greatly interested to see how it would play out. Is it tenable to place sovereignty in the hands of the people? Everyone had an opinion of some kind but no one was sure it could work, not even Americans. The U.S. at this time was subject to a devastating economic boom/bust cycle, was facing new social ills that resulted from urbanization (poverty, crime, drunkenness), saw widespread religious revival which often concerned itself with the concept of millienialism (the Christian idea that final judgment would soon be at hand), tension born of political issues like temperance and nativism/immigration and moral reform, not to mention that pesky slavery issue that was cropping up again. The U.S. seemed to be at risk in the eyes of many Americans.
Further, Americans were heavily opposed to engaging, as a nation, in the diplomatic and international power games that European empires were constantly involved in. They had been since the Constitution was ratified. What's more, when it came to European revolutions, they'd been hurt before. The French Revolution, very early on, had looked to Americans like promising republican reform. When it turned violent and chaotic Americans were shocked. They were optimistic about the spread of republican governments, but also wary of how horribly they could go wrong. (Haiti's revolution in the 1790s was probably on their minds too as a revolution from below which, in their eyes, went horrible wrong, though racial attitudes complicated that issue a lot as well).
So, 1848. In concept, Americans loved the idea. Pro-republican and pro-democratic change in Europe! America's shining example inspiring the Old World! Europe's imperial posturing and balance-of-power diplomacy might come to an end! Yay, yay, and double yay! I investigated newspapers in (what was then) a po-dunk Indiana town and found those sentiments everywhere when describing Hungary and the charismatic leader of its revolution, Lajos (Louis) Kossuth. But there were also other subtexts which basically expressed relief that there was an ocean between the U.S. and these changes. An Indiana newspaper article said "happily, America cannot be disturbed by any of these predicted events, although her trade and commerce may suffer somewhat." The majority of Americans wanted to watch and celebrate these changes from afar, and little else.
This is reinforced by the aftermath of Hungary's revolution. Basically, the Austrians sent in their army, along with another army from Russia (monarchs helping each other out), and crushed Kossuth's forced. Kossuth wound up in a Turkish prison, but then the US government arranged for his release and sent a ship over in 1851 to bring him to the US. Kossuth was the second foreign national ever to be officially invited and recognized as a guest of the United States. The first was Marquis de Lafayette who, you'll recall, was kind of a big deal in the American Revolution.
Kossuth's arrival was a little like the arrival of the Beatles in 1964. His boat was greeted in New York City by a cannon salute and a crowd of over 200,000 people. He tried to address the crowd, but they cheered so incessantly that no one could head him. When he tried to move through the crowd, fans used knives to cut away swatches of his clothing as souvenirs. He would soon embark on a nationwide 7-month speaking tour. Newspapers praised his commitment to Hungary's cause and liberty in general and obsessed over this man, his wife, the horse he rode, and the clothes he wore. Kossuth's beard and the distinctive feathered cap he wore both became fashion trends.
And by the end of his tour, much of his support was gone and he left the US quietly under a false name. What the hell happened? In short, Kossuth asked Americans for actual help. Kossuth overtly called for the resurgence of the revolution in Hungary, and Americans loved that idea. But then he directly asked the US government, then the populace, for help arming and financing his efforts. He definitely got some donations, Americans' views varied, but the majority had no interest in getting officially involved with European conflicts and politics. They wanted good enough relations for free trade, a policy that imperial powers often resisted, but that was about it. If Europe turned republican, great--but the majority of Americans did not want to get involved. It didn't help that Kossuth's original revolution had turned fairly bloody. When Kossuth kept asking, getting more and more insistent, and then making a few comments about American political issues like slavery, it was game over.
At least with Hungary, Americans thought 1848 was basically the best thing ever for Europe...as long as it stayed in Europe.