Do Americans really understand this two-pronged economic problem?

[Mister Chartreuse]

America is in the process of recovery from one of the worst recessions in its history. At the same time, the national debt has bloated to gargantuan size.

If the budget it "balanced" and spending is cut to the point where debt can begin to get paid off, America will plummet into another recession (since government expenditure is, at this time, an extremely significant portion of the country's GDP). While, theoretically, monetary policy and the private sector could eventually close this resultant recessionary output gap, there is really no telling how long it would take and what the full extent of the social consequences would be.

If the budget remains unbalanced and the debt continues to increase, America's credit rating is sure to continue to be downgraded by S&P, severely hurting foreign investment and decelerating long-term economic growth.

If you had to choose between these two, which would you pick. Is there a happy medium? If so, describe it in detail.
@T. Pain
Not really. Revenue might increase (arguable), but this would constitute a negative aggregate demand shock - decreasing the GDP; although, I will acknowledge that these individuals in these higher tax brackets likely save a larger portion of there money, so the economic consequences would be lesser than those of a general tax increase.

Still, it certainly won't solve the problem.
@The 1%
Cutting government spending does not necessarily create a "depression"; depending on the shape of the economy, government spending actually should be cut for economic benefit. However, in this shaky recovery situation, cutting government spending would have short term consequences (this is theoretically inarguable).

Personally, I am leaning more to the "bite the bullet" budget balance plan, letting the economy crash and employing monetary policy to fix the situation like you suggested.