Even the "make work" projects will provide jobs now and put more money into the economy (through indirectly created jobs such as restaurant workers - more employed people = more people eating out). Spending on retraining won't do much good without actual jobs. Mortgages can be addressed by a separate bill.
I think this is pretty much the heart of the problem. If you take 100K from rich person A and pay it to person B to pick up trash in the local park you say that's putting money into the economy but I say that those indirectly created restaurant workers are no different than what would have been created if person A had spent the money on whatever he/she wanted. If person A buys a jet with the money then someone still has to build it and that person still eats out etc so I just don't see how there's any net economic gain. There may be some intangible gains like the fact that you and I gain more from a cleaner park than from some rich guy's jet but that's not an economic gain that actually grows the economy.
The nice thing about retraining and education is that it better matches the available workers with the available jobs and thus improves efficiency and grows the economy. Consider a simple thought experiment. You've got a guy who spent the last 20 years operating a B210 series crane in Detroit. He's really good at it and makes 100K but due to the lack of commercial building he's out of the job and there just isn't anyone else who needs B210 operators within driving distance. He's basically screwed. Even if there's a job opening in Texas he can't afford to pay his current mortgage as well as rent in Texas so there he sits on unemployment. Is it more economically efficient to pay him to pick up trash or is it better to train him to do something that takes advantage of his excellent hand-eye coordination and trustworthiness? Even during training the indirect jobs will still be created (he'll be employing teachers) so there's no loss there but when he's done he'll be contributing more to the economy.
That's my take on it. What am I missing?