If the U.S. does not raise the debt limit in the short term, it will start to default on portions of its debt, and will see interests rates rapidly rise. The rising rates will increase the cost of rolling over existing debt, causing more default, raising rates further, and ... you get the picture.
If the U.S. does not cut spending by trillions in the medium term, it will partially default on most of its debt. The only realistic public policy result of the current spending trajectory will be sustained inflation of the dollar, lowering the wealth of anyone owning dollars or dollar-denominated assets (except TIPS). This would hurt the Chinese government and Americans who have saved for retirement or college. It would benefit the American government and Americans who have credit-card or mortgage debt. It would also raise interest rates on government debt issues to 19th-century levels and effectively cripple the government going forward.
Are there alternatives? Massive tax increases would cause a bigger recession than the recent one, and further lower tax receipts, so that's not a realistic solution for closing the deficit gap, although closing loopholes and capping exemptions would be smart.
Massive spending decreases will be painful, but are possible, if begun soon and stretched out perpetually. Leaving Afghanistan and cutting military spending commensurately is the first and most obvious of these cuts. Preventing Medicare and Social Security costs from ballooning in the next ten years is the next-most-obvious.
If this Congress and its successors do not find the courage to address the debt crisis, it will spiral beyond their control in ways they cannot imagine. The foolishness of the stimulus package - some of which still has not been spent! - is staggering in light of the current budget outlook.