I've been reading about how a job creation program would disrupt the private sector. One of the main things I kept seeing was that the a FJG will result in the elimination of thousands of jobs. So, consequently it would hurt the economy. But a FJG would create jobs that pay higher than minimum wages as well. Wouldn't that increase consumer spending, cancelling out the negative impact?
Conventional economics research is not very kind to the idea of job guarantee (see discussion in highly cited works of Palley, 2001; Sawyer, 2003 and Seccarecia 2004). In general most of the profession agrees that job guarantee program (i.e. program where government is some sort of employer of last resort/provides employment) is generally not efficient from either macroeconomic or microeconomic perspective, with emphasis on the macroeconomic perspective.
The problem is not that it would destroy jobs on a net basis. The whole aim of such program is to create government jobs for anyone that is unemployed so on net basis it would increase the number of jobs. The problem is that especially if the wage for these jobs is set at above minimum wage, or more specifically market wage at each individual sub-market it would crowd out productive jobs from the economy and instead create less productive government jobs (see the papers cited above).
Next unless this is founded by debt or high powered money it will not increase consumer spending on net basis. This is just elementary macroeconomics, if government runs balanced budget government spending multiplier will be exactly equal to 1 meaning it will not create any additional stimulus for the economy and even that assumes government funds itself with non-distortionary lump sum taxes so in reality it would likely depress demand (see Blanchard et al. Macroeconomics: a European Perspective).
Now, in principle there is nothing wrong with government running deficit or financing projects with high powered money but both are not suitable for some large permanent program. When it comes to financing projects with high powered money there is virtually unanimous agreement in the profession that only limited amount of real spending can be financed in such way (see this poll among top US economists). There is also issue that amount of real spending that government can finance with high powered money depends on macroeconomic situation (e.g. more of it can be financed when interest rates are zero and less otherwise). When it comes to deficit it is generally considered desirable to run budget deficits in recessions, but in the end government needs to respect its intertemporal budget constraint so in expansion it also should run surplus (technically thanks to economic growth there is some leeway as if we assume there are no 'end times' when debt has to be repaid, government could run deficit equal to rate of growth and keep its debt-to-GDP ratio stable - but with GDP growth rates most developed nations have this would only give extra leeway of about $1-2\%$ hardly enough to fund some ambitious program).
Lastly, issue with job guarantee program is that anything it promises to do can be done better in some other way. If you want to raise welfare of the poor then there is a plethora of relatively more efficient redistribution policies. If your aim is solely boosting employment then there are many other policy instruments such as earned income tax credit, which in combination with minimum wage can boost employment while creating also some floor below which peoples' earnings can't fall. If your goal is to stimulate economy then simple fiscal stimulus to households would be more efficient etc (you can see overview of this in the above cited literature). Hence, most conventional economists would reject job guarantee on the grounds that there are more efficient alternatives.