It's just as easily to set up a useless, profitable company as it is to set up a useless government branch. So the assumption that the taxed area of the economy is productive is somewhat suspect. It's in fact possible to set up large, destructive, private bureaucracies that turn a profit. Our mounds of financial regulations do their best to make that hard, but the fact is people still make a lot of money doing it. Wealth creation and profit are two very different things.
Giving people pointless jobs creates stability, which in many cases is more valuable than any sort of physical good.
And let's remember that the argument in favour of government work programmes isn't solely to be contrasted with not-spending-the-money... it's to be contrasted with welfare.
So the society/government has, broadly speaking, three alternatives (and a continuum therebetween):
* Do nothing for the unemployed
* Give the unemployed some money
* Act as employer of last resort
Doing nothing acts as less drag on the productive aspects of the economy, and also it's really easy to implement. The downsides include civil unrest, and also arguably have long-term negative consequences on the productiveness of the entire workforce (compare with economically-inefficient government subsidies of shipbuilding in nations that wish to maintain the ability to go to naval war, e.g. the US).
Giving them money eases the civil unrest problem. Yay, less revolutions! And hopefully for people who go through temporary rough spots, it permits them to reenter the productive workforce, instead of falling into inescapable poverty. The main downside is screwed-up economic incentives for the unemployed.
Work projects have no greater drag on the productive economy than EI, but might have less drag. Also, they act as work experience, and they eliminate the wicked incentive for the underemployed workers. BUT, they create screwed-up incentives for the employers, who now have a source of cheap labour, which they are now incented to victimize. (Compare with the incentive problems with US for-profit prisons.) Work projects may prevent recipients from seeking new better jobs (through being busy during the workday). Work projects compete at the low end with non-government-run businesses, in ways that are sometimes seen to be economically troubling (I don't follow this argument, myself).
So, sometimes the arguments against work projects also apply to 100% subsidies: "that's anti-capitalist, anti-competitive, pinko commie socialism". But there are some other arguments that the left levy against work projects, like the victimization/incentive issue.
Giving people pointless jobs creates stability, which in many cases is more valuable than any sort of physical good.