When the economy needs short-term demand stimulus, as it does now, that stimulus can come from spending on infrastructure, i.e. government investment, or it could be from expenditures on something with little long-run benefit such as large fireworks shows held throughout the nation - big extravagant events that spend millions and millions of dollars in the most depressed economic areas (government consumption). In the short-run the goal is to kick start the economy, and a fireworks show is just as good at that task as infrastructure spending if the spending is approximately the same.
Where they differ is in the long-run. The firework show leaves only memories - and sometimes that's enough to justify an expenditure - but let's assume that for the most part the shows were nothing more than an excuse to spend money to get the local economies moving (not that there's anything wrong with that; also, perhaps a series of shows would be better so that the impulse is spread out over time and sustains the economy through the downturn, but the idea is the same). However, infrastructure spending does have long-run benefits and can help the economy grow faster.
Thus, it seems like infrastructure spending is the obvious choice, since it has both short-run and long-run benefits. But there is a further consideration, how fast each type of spending can be put into place. If a "fireworks show" can be put into place very fast, while it takes far longer to get infrastructure spending going, then policy should be a combination of spending that hits the economy right away (government consumption) and spending that hits a bit later, has long-lasting effects, and promotes future growth (government investment).
Then there's the politics. Conservatives often oppose government consumption (e.g. by arguing the multiplier is zero even in depressed economies, by arguing that tax cuts that allow the private sector to spend are more efficient than government spending, or arguing that our debt is too high to spend any more). But what I don't get is why conservatives have gotten away with opposing infrastructure spending to lift the economy. Infrastructure spending is inherently a supply-side policy, both sides acknowledge that, or should, and some of us believe it also short-run demand effects that are also helpful. But whether or not infrastructure spending impacts aggregate demand, it seems pretty clear given the state of our infrastructure that the benefits of this spending just in terms of the long-run effects more than cover the costs. And the argument that the private sector does it better doesn't hold since most of this spending is on public goods the private sector will not provide in sufficient quantities if it provides them at all. Finally, we can afford to borrow today to fund investment projects that have long-run benefits that exceed the costs.
But yet, here we are with an unemployment crisis, a huge output gap, and big infrastructure needs, while Congress sits on its hands because conservatives will not agree to fund infrastructure, let alone government consumption spending.
I find it very frustrating.