The major problem facing the U.S. government today is raising the statutory limit on the national debt. Doing this is both urgent and routine -- Congress raised it seven times during the presidency of George W. Bush alone -- and never before has either political party taken the process hostage as the Republicans are doing. (When there was even a slight hint of this in the 1980s, President Reagan argued correctly that it would be an incredibly stupid and dangerous thing to do to the country.)
A nation's debt certainly lead to a crisis -- just look at the situation in Greece and Ireland and looming problems in Spain and Italy. But by any rational measure, the current U.S. debt situation isn't a crisis (our debt load is nowhere near that of Spain or Italy, let along Greece or Ireland), and it isn't hurting the economy. We have economic problems, but it's clear that the debt isn't causing them.
There are basically two ways in which the national debt can harm the economy. The first is for government demand for money to drive up interest rates, making it more expensive for businesses and individuals to borrow. But both short- and long-term interest rates are currently near record lows, and the only reason we might see higher ones is if credit rating agencies cut our bond ratings, as they say they will if Congress doesn't raise the debt ceiling.
The other way is for borrowing to grow so big that making the payments soaks up the government's available funds, causing it to either raise taxes, cut expenditures, or both. Since the government is a major employer and a major customer for the private sector, cutting government spending slows the economy essentially by definition. Likewise, raising taxes reduces private spending, and that harms the economy as well. (This isn't controversial. Conservative economists who want to shrink government spending acknowledge that doing so hurts the economy; they simply think the economic pain is worth it in the long run.)
The sad thing is that just ten years ago we were running such large surpluses that the Congressional Budget Office projected that the net national debt would by now be close to zero. What happened? In brief, three things:
First, George W. Bush took office and pushed through massive tax cuts favoring the rich. Then a year later he did it again. (Reportedly, it should be noted, he did agreed to the second round of cuts with reluctance and only under pressure from the right wing of his party.)
Second, we got into two very costly wars. The overthrow of Afghanistan's Taliban government was at least somewhat justified, but serious mistakies turned it into the longest war in U.S. history. The Iraq war, which contributed to the failures in Afghanistan, was a mistake to start and then badly botched.
Third, the safety features introduced into the financial system in the 1930s, a set of reasonable regulations that had prevented financial crises for half a century, were dismantled, starting under Ronald Reagan. The first major result was the savings and loan crisis of the 1980s, which cost taxpayers sums that at the time seemed staggering. (If only we'd known...) This deregulation mania continued under George H.W. Bush, Bill Clinton, and George W. Bush. Basically, the people making huge profits from deregulation -- profits from risking other peoples' money -- poured lobbyists and money into Washington and corrupted both parties. When the financial system collapsed in the last year of Bush's term it took much of the economy down with it.