I'm not really an economics guy myself, so I won't comment on Keynes, Mundell-Fleming and the other economists' theories.
As far as I can tell, the only really obvious ways to get out of debt are to cut services or raise taxes, or both. If you hike taxes, you take money out of the economy - the taxpayers don't have that money to spend or invest, and the government isn't building anything or employing anyone with the money - they're just paying off debt. So the risk with hiking taxes is that you will slow down the economy or even trigger a recession, which will cut your tax base (a recession will cut taxpayer income).
Cutting services is risky too - the government employs a lot of people. If you cut services, people will be out of work. People out of work can't pay taxes and compete for private-sector jobs, driving down income and boosting unemployment. And people out of work aren't spending or investing (as much as they used to) either. Some government spending cuts impact the economy less than others, of course - cutting foreign aid, for example, would have a smaller effect on the economy than cutting a domestic infrastructure program that 1) employs people and 2) produces a finished product that will help the country, and economy, function more efficiently (hopefully). Military spending is generally a pretty inefficient way to stimulate the economy, because the finished product doesn't produce wealth or make the economy run more efficiently.
(and of course, cutting spending hurts people who depend on the programs being cut - social security, school lunches, and the like)
A lot of the foregoing are generalities, of course. But the only reasonable ways to eliminate a debt are raising taxes and/or cutting spending. Printing more money (inflation) and defaulting can produce some unpleasant side effects...
The trick to raising taxes/cutting spending is to raise the
right taxes and cut the
right spending. Some believe that if you reduce the taxes on the very wealthy, the very wealthy will take their tax savings and invest them in the economy, thereby creating jobs. There's another school of thought that if you cut the taxes of the wealthy, the wealthy can just as easily invest their tax savings offshore. I personally fall into the second school -the wealthy are more mobile than the poor and the working class, so they're less likely to spend or invest locally than the poor and/or working class are.