Keynesians seem to love government debt. They wouldn't exactly put it that way, but that is the only conclusion one can come to after listening to most of them. They will say that the debt doesn't really matter much and that any negative effects are more than offset by the positive stimulating effects on the economy.
Supply-siders can vary in opinion on government debt. When a Republican is in the White House, they will typically say that debt doesn't matter much, as long as we enact policies where we can grow our way out of it. If a Democrat is in office, then they are more likely to criticize government debt as being a burden on future generations.
Austrian school economists (advocates of free market capitalism) are consistent in opposing government debt. While I am completely against having any kind of a deficit, I do agree with Ron Paul in that the overall spending matters. I would rather see a deficit with a $1 trillion per year budget, than a balanced budget where the government is spending $4 trillion per year.
Austrian school economists do differ in how they view the overall debt and its effects on prosperity and future generations. There are also differing views on how to deal with the debt. Some say we should pay it down or grow our way out of it. Others say that it should all be repudiated (meaning a default).
My opinion (although I think it is fact) is that government debt burdens future generations only in the sense that it currently reduces savings and capital investment, which will mean less advancement in technology and capital goods for the future.
If future generations continue to honor the debt previously run up, then it will cause a redistribution of wealth, but much of the redistribution will occur between individuals. Even debt owed to the Social Security fund will mostly end up back in the hands of individuals and not spent by government. This would be the worst case scenario for future generations. More likely though is that much of the debt will be repudiated, whether deviously through inflation or outright default.
But let's forget future generations for now. That is what most people seem to discuss when talking about the dangers of high debt. But where it matters the most is right here and right now. The government debt is what allows the government to spend massive amounts of money. There is no way that the government would be able to raise taxes enough to pay for all of its spending, so it must resort to debt. Without a central bank and fiat currency, lending would be very limited and interest rates would quickly rise with high levels. But because of the Federal Reserve's monopoly over the supply of U.S. dollars, it enables the government to accumulate massive amounts of debt and spend what otherwise would be almost impossible.
So what most people fail to understand is that the massive deficits make us poorer now. It hurts our standard of living. It is because government is able to spend huge amounts of money.
Why is this so harmful? It is because virtually everything the government spends is a misallocation of resources. Even if politicians really did care about the little people, they would have no idea how to quantify the wants and needs of hundreds of millions of Americans. So while not all money spent by the government is completely wasteful, it is almost always wasteful in comparison to how it would have been used by those who earned it.
In conclusion, government debt does matter. But where it matters the most is here and now. It allows the government to misallocate and waste resources on a massive scale. We are all poorer because of it.