Become employed doing low-wage non-unionized government work, same as the private sector unemployed. The government can produce more for less money.

Of course, this assumes that producing services is the government's actual goal. If funneling money to cronies (politically connected corporations, government unions, etc) is the goal, then this method won't accomplish that one so easily.

Get jobs that actually help the economy. The government can't add jobs to help the economy by definition, because they don't work in the realm of profit/loss. This is called the economic calculation problem. We've ignored this problem, and that's why we keep creating jobs from stimulus while losing twice as many as created.

Huh? Aren't government employees paid in the same currency as employees in the private sector? Don't those employees spend that currency largely in the private sector? If those people wouldn't otherwise be employed, how are their jobs not "helping the economy"?

You are propounding the Broken Window Fallacy. To discover the flaw in your reasoning see:

http://bastiat.org/en/twisatwins.html

It looks to me like this is only a fallacy on the assumption that government employees are like glaziers fixing broken windows: absorbing value that, but for a loss, could otherwise be put to another use. It is that assumption that I meant to question, though I see I did not express the point adequately.

If you wish to question such an assumption, you need to show that government employees produce something of value, not that they consume something of value.

I think the people at the DMV produce something of value. They limit who's allowed to drive making the roads safer. That is extraordinarily valuable.