Belgium's public debt came down from 130 percent of GDP to about 85 percent in less than 15 years (though it went up again after that due to the financial crisis and all that). The USA is not Belgium, but if anything it tends to have a somewhat higher GDP growth percentage, so it could achieve the same percentage reduction in debt with a smaller percentage saving in spending. Balancing the budget for a number of years in a row would bring the debt back to manageable levels of GDP fairly quickly - something in the 60 percent range or so, which is the number usually mentioned as target. Aiming to eliminate public debt completely is pointless.

The problem is not the debt as such, but the huge part of the American budget that is widely considered off limits for cuts - Social Security, Medicare and Medicaid, and then in a different category the national defense expenses. If you're going to balance the budget without touching any of those sacred cows, then I agree that's not going to be doable. But once you move beyond the dogmas and are open to look at everything, it's not that hard anymore.

A partial default without reforms that ensure budgets can remain more or less balanced in the long term is completely pointless as the debt would just grow right back, and it would drastically increase the cost of the debt that remains. If you do have the reforms, there isn't any need for defaulting on anything. So either way it's a terrible idea.