Money does not know from whence it is spent. When somebody goes to that privately owned sandwich shop the dollar coming from the police officer, the teacher, the senator, court clerk, postal employee, or immigration officer is no different than the dollar coming from the private lawyer, doctor, actor, engineer, or real estate broker.
Moreover the government worker taxpayer dollar spent is no different than the private company worker dollar spent. Its origin is always the citizen. For the government, the citizen paid taxes for services and security provided. For the private company, the citizen paid for some service or product.
When that sandwich shop owner uses that dollar to buy bread, meats, vegetables, and government services (e.g., taxes for the road the customer used to come to his shop, quality control on his meats, etc) employment is created or maintained to keep the cycle going.
How does government create jobs then? It is no different than any private large corporation like Exxon, Siemens, etc. They can hire to provide a product or service to their customer/taxpayer. Interesting enough the same problems that afflict the government because of its size, also afflicts these large corporations. They are not nimble.
As a country we have decided that we want the private sector to be the engine of job creation because decentralized innovation in many areas is more agile and more productive. Large regulated corporations are more efficient in providing certain products and services like oil production, mining, etc. Government is best for providing product and services where no innovation is required (healthcare insurance for all its citizens). Ideally most other products and services should be provided by small & medium size private companies and individuals (hospitals, doctors, restaurants, etc).
Our current corporate control government and economy has made the system unbalanced. A few large corporations control our media that misinforms us into supporting policies that transfer our wealth to a few, control our means of production that leave us at their behest, control our patent system that stifles innovation of the average citizen, and outsource our labor for the gain of a few.
Corporations are not creating jobs because they do not have to. They are profitable and content with the current state of unemployment because it is unlikely that the government will either increase their taxes or induce the Federal Reserve to increase interest rates. Supply and demand along with massive outsourcing will keep wages down until the unemployment rate improves. In a time like this government must create jobs. There is a lot of work to be done on our infrastructure, education, alternative energy, and other areas. If private corporations won’t, then government by and of the people must.