Let’s assume that $100 pays for 100 jobs that create 100 goods. For our purposes it doesn’t matter who spends the money: the jobs will occur and the goods will be created. It does, however, matter how the money is obtained.
In the private sector, the $100 must be accumulated through productive industry — that is, by creating goods. Government, however, obtains the $100 by subtracting it from the private sector. Thus, for government to spend $100, the private sector must spend -$100. By virtue of subtracting the $100 from the private sector, the government can never produce, on balance, more than zero goods.
It is possible for the goods government creates to be beneficial. Roadways and water systems are examples. But notice two things: (1) the subtraction of money from the private sector still occurs, and (2) it is not inherently or necessarily the case that the government-created goods are better than the private-created goods would have been, had they been created.
Various other considerations are in play. For example, government can create money to spend without subtracting it from the private sector. In that case, government gets the benefit of spending $100 to create 100 goods without offset, except that the $100 then becomes an increase in the money supply, which causes a corresponding amount of monetary devaluation that the private sector will experience as an equal material loss (-$100, or -100 goods).
Another example: Some government spending is inherently non-productive. Broadly speaking, military spending is in this category. Despite being necessary and desirable, the defense industry literally produces no goods. Consequently, the $100 that pays for 100 jobs and produces zero goods on balance (after accounting for the private sector losses) actually creates -100 goods on balance when government uses it to fund the military.
The takeaway here is that it matters after all who spends the money because the implications are different based on how the money is obtained and then spent. It is one of the greatest tragedies of human experience that many people think government can do good easily. Government can certainly do good, but not easily, as some dreamers imagine.