First of all who says debt is a problem? There is much debate on this. A nation does not work like a business or a household. Actually quite the opposite. Debt can be good. And right now a lot of people really, really want to give their money to the US government for safekeeping, because they think the best and safest investment is the US government. Therefore interest rates for borrowing are very low. There are other reasons why debt might not be such a huge issue. As I said, this is really up to debate.
Personally I believe that the rate is borrowing is, in fact, a little high right now.
But this is not about borrowing, but about spending. A lot of people in Congress want to spend money on different things. And they don't want to raise more income. So they have to borrow. The problem, if you are concerned about debt, is not the debt ceiling, but the spending and income.
The debt ceiling is mainly about bullying the president. It's a bargaining chip. It's only about politics.
But no one wants to talk about which programs to cut exactly and which taxes to raise, because this is unpopular. This applies to all players.
The ironic part is that the Republicans are making a huge deal out of the debt (I said at the beginning that debt doesn't have to be bad), while they are being responsible for it through defense spending and tax cutting during the Bush years. And they never had a problem back then.