I don't think the idea that the unemployment problem is mostly structural stands up to the evidence, see here for example, but for the sake of argument suppose it is. How should we respond? There are several choices:
1. Do nothing to help. Even though the problems facing the unemployed were created by events out of their control -- they did nothing to deserve unemployment and the struggles that come with it -- and even though those who did cause the problem have received lots of help from bailouts, unemployed workers should not get anything from the government. They're on their own.
2. Provide government help in the form of transfer payments (i.e. cash or the equivalent, e.g. food stamps, from the government), but don't expect anything useful in return. Just send checks and vouchers.
3. Provide the same amount of support as under 2, or better yet even more support, in return for jobs that do useful things for the community. That is, bridge the time while structural adjustments are underway with useful employment for those waiting for the structural changes to be completed.
4. Provide job retraining, use tax incentives to promote better matching by inducing workers and firms to move, and implement tax and other incentives that encourage more business investment and hence faster adjustment from firms.
Importantly, with cyclical unemployment there is also a fifth option, increasing aggregate demand, that does not exist when the problem is structural. But if we cannot increase aggregate demand sufficiently due to political or technical reasons, we also need to bridge the gap while demand recovers by providing jobs for those who will not be able to find employment no matter how hard they try.
To me, the choice is easy. For long-term structural unemployment, 3 is best. There is an argument for 2, we want workers to have the resources they need to search for jobs that suit them best, so we shouldn't eliminate this type of help. But the structurally unemployed will not be able to find a job easily even with an extended, dedicated search supported by unemployment compensation. They need jobs to provide income for their households and to keep them connected to the labor market.
But there is one potential caveat to a jobs program for the structurally unemployed -- it might reduce labor mobility. Workers who might have been inclined to move to take a new job will be less inclined to do so if they have a temporary, community value enhancing job from the government. I don't think that's a significant worry even when the problem is largely structural, but it's worth noting. (Remember that I am assuming structural unemployment for the sake of argument. If the problem is mostly cyclical, as I think it is, this isn't an issue.)
But even if reduced mobility is an issue (and, again, I don't think it is), there is an important offsetting effect. Long-term unemployment, the type that occurs with slow structural adjustment, has long-term negative consequences for the economy (and this is true for both the cyclically and structurally unemployed). The longer people are unemployed, the higher the chance of them dropping out of the labor market permanently. Workers close to retirement will find a way to hang on for a few years by living with family, doing odd jobs, etc., and their experience and skills will go to waste. Younger workers tend to drop out, or work in the underground job market, e.g. doing construction outside of the formal job market. Or they take whatever job they can get and then buy a car, a house, have a kid, etc. and get stuck in a job that does not make full use of their capabilities. They are part of the long-term under-employed. We are all worse off when this happens. The point is that long-term unemployment causes the labor force to erode in both numbers and skill, and that is costly to society. Simply keeping workers connected to the labor market with a job of any type -- doing things the community needs for example -- avoids the erosion of the workforce and the negative consequences (lower economic growth rate) that come with it.
Thus, contrary to what you sometimes hear, we can help the structurally unemployed through job creation. Those who insist, contrary to the evidence, that the problem we face right now is mostly structural cannot use this to argue against a job creation program. In fact, since increasing demand is unlikely to work in the case of structural unemployment in the way it will for a cyclical problem, there is a sense in which the argument for job creation to bridge the long adjustment gap is even more compelling when the problem is structural.
So it doesn't matter whether the problem is the inability to offset the slow recovery of demand through monetary and fiscal policy due to political or technical problems, or long-term structural adjustment, we need jobs, jobs, jobs.