The risk of regime change
If rates move up dramatically, however, the cost of financing the debt will go up and pressure the deficit, as higher debt servicing costs will either crowd out other government spending (unlikely) or increase the deficit further (compounding the problem).
For this reason, I think the Fed will be cautious in its tightening approach, with an eye on the “terminal value” of rate hikes. It can steer short rates directly, but shorter-term Treasury bills constitute a little less than 20% of the debt. To influence longer-term rates, it can use policy and language (e.g., anchoring short-term rates for an extended period). Quantitative easing (buying bonds) can have a more potent effect.
The risk of this approach is inflation. If cautious tightening yields high inflation, the Fed may still seek to keep rates low, but buyers (other than the Fed) might decline to buy Treasuries at the rates offered. If the Fed becomes the buyer of last resort to finance Treasury borrowing, we could have a scenario where the Fed is essentially printing money to fund the federal deficit, which would almost certain bode poorly for the US dollar and, eventually, the economy.
In short, this means that in the years ahead, the Fed will have to plot a course between rates that are too low (keeping the debt and deficit in check but risking inflation) and too high (keeping inflation in check but posing the risk that the debt and deficit become unbounded). I’d note that as much as I am concerned about the idea that higher rates could destabilize US fiscal footing, I balance this with worry on the other side that we might head into a Japan-like, permanently deflationary environment where the size of the debt becomes almost irrelevant.