There may be civil unrest in the United States due to the nature of the programs they are cutting. They aren't cutting out massive military budget, which is half of the world's military expenditures, but they are cutting social programs that help poor people and give the elderly a better quality of life.
It may not come about in violent manners or as an extrerme outburst, but civilians will certainly be upset and discomforted by US fiscal cuts. At the same time, there are those who ideologically support the fiscal cuts, so these people will not have unrest at all. It should even out, but the vocal minorities typically get the most attention.
I believe if more programs within the United States experience more fiscal cuts, there is a possibility of civil unrest. There is a portion of the American government that is supported by the government because their employers refuse to pay a responsible living wage. If the government doesn't support these people they will be left to starve. That's not going to go unchecked.
While making cuts to certain programs will end up angering people I don't think it will bring any widespread civil unrest, normally these cuts are targetted at wasteful areas that would not effect the majority of people anyways, those programs that are vital to people are usually left untouched in any cuts.
Fiscal cuts will not lead to civil unrest. Civil cuts are what is needed in this country in order to give the tax payers some of their money back. Most of the population of the United States wants the government to spend less money and let citizens have some money back.