Suppose someone - say, the president of United States - proposed the following: We are drowning in debt. More than $14 trillion right now. I've got a great idea for deficit reduction. It will yield a savings of $230 billion over the next 10 years: We increase spending by $540 billion while we increase taxes by $770 billion.
He'd be laughed out of town.... makes me think not so much that Republicans have forgotten arithmetic, but that they have never learned basic accounting identities. You see, the thought espoused by Mankew (who is an economist, for chrissakes!) and Krauthammer originates in the confusion between the pocketbook of the citizenry and the pocketbook of the government. They think that the two move in tandem, where, in fact, it's exactly the opposite. They think that lowering taxes helps the people save money (true!) and therefore also helps the government save money (absurdly false!). And they think that goverment spending increases government borrowing (true!) and therefore also increases the debt of each citizen (also false!).
It's easy to see how you make the leap - after all, aren't the debts of the government our collective debts? That's intuitive but also completely wrong. The Govenment is the ultimate accounting counterparty to each of us individually, rather than a contiguous entity whose assets and liabilities can be meaningfully consolidated with each of us. Government debts are assets of those who own them - i.e., the people* (*ignoring foreign governments and corporations for the time being). Money is, fundamentally, a demand promissory note of the government (or an ultra-short-term government debt). So when the people try to save (increase their assets) the government has to borrow (increase its liabilities). And vice versa.