By creating public work projects (it could be federal or state level) it can create temporary jobs for unemployed and homeless people. This way they are providing something to the community while being able to support themselves and look for permanent employment; it would get people two can and want to work able to and only allow welfare for those who truly need it.
Read Paul Krugman's "End This Depression Now!". It's a call for Governments to implement Keynesian policies, aka, government expenditure. By doing this it creates jobs, thus lowering unemployment, increasing spending and demand and therefore helping the economy. However, as Krugmans book shows, when Obama, spent $800 billion on 'stimulus' it was mainly on welfare and benefits not on creating jobs and this really didn't help the economy very much. Therefore, following Keynesian theory, the Government should spend money on creating jobs through public works projects as FDR did in the past and showed it worked.
There are not enough jobs for every unemployed person. The private sector has never and can't be expected to provide one for everyone. So public work programs are needed. Welfare is also needed because there are plenty of people with jobs that live in poverty. So there needs to still be welfare to support people with and without work. (Without work for whatever reason).