Add to that the monumental costs of rehabilitating North Korea, which under the best circumstances would cost at least $1 trillion (the estimated costs of reunification) but which would balloon up to $3 trillion in the aftermath of a devastating war. Ordinarily, South Korea would be expected to cover these costs, but not if that country too had been devastated by war.
Spending on the military campaign and on post-conflict reconstruction would push U.S. federal debt into the stratosphere. The opportunity costs — the funds that could have been spent on infrastructure, education, health care — would be enormous as well. The war would likely put America into receivership.
Bottom line: Even a limited war with North Korea would directly cost the United States more than $1 trillion in terms of military operations and reconstruction, and considerably more indirectly because of setbacks to the global economy.