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The counterintuitive part is that a lower Fed rate doesn't necessarily mean cheaper borrowing for the government. The Fed sets an overnight rate; someone lending for ten years cares about inflation and interest rates over those ten years. Keeping short-term rates low won't necessarily reassure that lender. [1]
It also helps to distinguish the government's debt from a giant credit card. Existing fixed-rate bonds keep their agreed interest payments. Higher borrowing costs feed into the budget as old debt matures and gets refinanced, and as new debt is issued. The pain accumulates rather than arriving all at once. [2]
Nor does a larger interest bill automatically require "printing money." Treasury borrowing and Fed money creation are separate decisions. [3]
The difficult question is how to contain inflation without causing more economic damage than necessary. A large debt load makes that tradeoff more expensive; it doesn't make either option painless.
[1] https://www.federalreserve.gov/monetarypolicy/monetary-polic...
[2] https://www.treasurydirect.gov/marketable-securities/treasur...
[3] https://www.federalreserve.gov/faqs/how-does-the-federal-res...