I'm finally beginning to understand what economists like Paul Krugman are getting at when they focus so heavily on the output gap. The output gap is the difference between what the economy could be producing if everyone who wanted to work were working in a way that took best advantage of their skills and what the economy is actually producing.
The economy's potential grows continually because (a) the population is increasing and (b) technology makes it possible to accomplish more with less effort. An estimate of the current rate of growth of the economy's potential is about 2.2%. That means that GDP must grow at that rate to keep up with population growth and technological advances. Any slower rate means either that people are un-/under-employed or that we are not using our skills and capabilities as well as we might.
Here's a graph (from EconBrowser) showing potential vs. actual.
It shows that our actual GDP is about $1 trillion (or 7%) less than it might be. The point isn't that material production is the most important thing. The point is that people who can and want to be productive don't have the means to do so. Not only that, but if given the chance to be productive, they would be, which would raise everyone's standard of living.
It is for this reason that Krugman and others urge that the Federal Government step in and provide "demand" to enable those people to work—and make everyone's life better. The waste that we are experiencing isn't necessary. So why put up with it? If there are people ready and willing to work, why not take advantage of that and let them do something useful. Why waste this potential when we don't have to?
Of course the question then becomes, what is that they should do? There seem to be two answers. One is to seed the economy with money so that the market—now that it has additional money—will determine how best to allocate that available effort. The other is to put them to work building stuff we know we need, like infrastructure creation and repair. The second is capital investment in society. It seems to me that that's a better way to put people to work. The existence of unemployment means that we have the luxury of upgrading out infrastructure. Why not take advantage of it.
Does government know what's the best infrastructure investments to make? Probably not absolutely. But we do want government to build some of our infrastructure. So it's not out of the question to expect government to build more of that infrastructure when people are unemployed than it would when the economy is functioning at full employment.