It is bad when it causes excessive inflation. The "debt" in itself can never be unsustainable, since it is denominated in USD, which is a floating fiat currency that the US government controls. The US government is the source of all dollars, so it can never 'run out of dollars'. However, printing too many dollars can lead to inflation. So the deficit could be called unsustainable if it causes unwanted inflation.
Debt does not (necessarily) mean high taxes in the future.
Deficit is Government spending - Tax collected. High deficits might lead to inflation. One way to control inflation would be to increase taxes(draining money out of the economy)
> In general, when the government consumes a lot, the private sector can consume less of the national product.
This is not exactly true. When there is still "slack" in the economy(it is not at full employment, the private sector isn't investing for other reasons etc.), government spending tends to have low inflationary pressure. It is only when the economy is operating at peak productive capacity that government consumption crowds out private sector consumption.
> Debt does not (necessarily) mean high taxes in the future.
You are right, that's why I called it another possibility. To list them all explicitly.
Higher debt now means that the future either has default, higher (than anticipated) inflation or higher taxes.
(A steady inflation doesn't do anything to debts: at the time the debt is incurred, any anticipated inflation shows up in the nominal interest rate. Similarly, getting a reputation for defaulting increases your nominal interest rate. A reputation for high taxes doesn't do anything to the interest rate directly.)
Responsible governments try to avoid default and ever increasing inflation. That leaves taxes. Or taking on less debt in the first place.
About slack:
Modern central banks target inflation. If there's slack like you describe, a competent central bank will inject more money until inflation is at the target.
Central banks wire their profits to the treasury. That includes the seigniorage income they make from propping up inflation back to the target.
That's just bog standard monetary policy. And doesn't crowd out private sector investment and consumption and is perfectly capable of picking up any slack.
(That's not to say the fiscal side of government doesn't have any effects at all. But that's more on the supply side.)
