Your model itself is a significant assumption, though. Consider the Clinton tax hikes combined with some moderate restrictions on growth in spending as a counterexample: they ultimately led to the closest thing to a budget surplus we've had in our lifetimes, ignoring details like whether we technically were in surplus or not.
It is fair to ask whether that's sustainable, as in the 2000s we saw our politicians take those projected surpluses and spend them on tax subsidies for the well-off. Which, indeed, is just what that model predicts. But that just speaks to the need to elect better politicians and create better institutions to act as an endogenous curb on unjustified spending.
Your tone suggests you think you're contradicting me, but your last sentence is simply a restatement of my point. (I'm still trying to work out a clean way of stating it, so I take responsibility for that.) The solution needs to solve the dynamics of the problem. It may visibly manifest as tax hikes and/or spending cuts, but those will be effects, not cause.
It is fair to ask whether that's sustainable, as in the 2000s we saw our politicians take those projected surpluses and spend them on tax subsidies for the well-off. Which, indeed, is just what that model predicts. But that just speaks to the need to elect better politicians and create better institutions to act as an endogenous curb on unjustified spending.