Disagree on multiple counts.
First - you don't need both - if you cut Social Security and Medicaid altogether, and use the surplus to start paying down debt, that solves 100% of the deficit and starts chipping away at the debt, while this would actually reduce taxes rather than raising them. I'm not asserting that the political will exists to do this (it doesn't), but the idea that you can't balance the budget without raising taxes is obviously false - taxes are nonzero, but you could reduce spending to zero.
Second - you don't actually need either - if you hyperinflate the currency, the value of the existing debt becomes negligible. To wit, I fundamentally agree with the message of the remainder of your post.