The Sunk Cost Fallacy is an economic idea which says that rational economic agents ignore costs already incurred in some endeavor and only pay attention to future or prospective costs. The point of the idea, like so many others, is to show how humans behave in seemingly irrational ways. Because the fact is that humans absolutely pay attention to sunk costs, all the time.
For example, research suggests that if I offer to pay you the exact same amount of money for a purchase you recently made, you will likely turn me down. The reason being that you have already incurred some sunk cost in aquiring the product beyond its monetary price. So, my offer to pay its purchase price does not mentally get you over the hurdle to accept my bid. In fact, even if I were to offer more than the original purchase price, you are likely to maintain your rejection of my offer. Economic theory says that you it shouldn't matter that you recently purchased something. If I offer you at least the purchase price you should be at least indifferent between keeping the product or selling it to me. But, research shows time and time again that folks have loss aversion tied to the idea of sunk cost.
There isn't anything controversial about this notion. In fact, in recent years economists have been rethinking the Sunk Cost Fallacy, to understand if it is even a fallacy at all. It seems perfectly rational to allow time or monetary cost spent to impact future decision making. Nevertheless, there is the chance still that paying attention to sunk costs is economically inefficient. In other words, that while paying attention to so-called sunk cost is rational, doing so may still lead to sub-optimal decisions. I believe that this is especially true if we consider public policy.
Let's quickly put aside the issue of debt for a moment, as it presents the most salient argument for paying attention to sunk costs. For now, let's just focus on the idea that the goal of public policy is to respond to dynamic economic scenarios with attentive and consensus driven political decisions. In this way, the goal of policy is to harmonize the society around us. This mechanism is more than imperfect, with policy makers at times choosing policies which actually lower social welfare. Regardless, the goal of policy is for the policy maker to choose the policy that they believe leads to social welfare augmentation, for whatever that means.
Sunk costs show up for the policy maker in two ways: 1) costs they chose and 2) costs they did not choose. Every politician begins their political career by taking the reins of a policy apparatus constructed by years and year of other people's decisions. Despite this, I'm willing to bet that policy makers are less susceptible to the sunk cost fallacy when they haven't made the decisions previously. For those politicians who are privy to the sunk cost and for whom are faced with considering the sunk cost that they created, it seems much more likely that they will figure those previous sunk costs in their future political decision making. So, if a politician enacts some large scale public projects, they may be less likely to push for other projects, despite their potential to improve the lives of their voters.
If we consider government debt, at whatever the level we want to, then clearly sunk costs are real costs. So, if that big project required debt financing, I think it's fair for a politician to consider this debt load when making future decisions. But, and this is crucial, the need to consider debt doesn't simply mean they may spend less in the future, but could also mean that they raise taxes to pay for future projects, thus avoiding the sunk cost fallacy. Nevertheless, most research shows that politicians are loathe to raise taxes, and so I suspect this makes them even more prone to suffering the sunk cost fallacy.