On top of this, the number of jobs is not a fixed number. The workers who lost their jobs in manufacturing can be more productive in other jobs, which benefits everyone. Also, money people save by purchasing cheaper products is money that can be spent elsewhere, increasing demand for other goods and thus supply, which means more workers in other areas. By only looking at the smaller picture losses (manufacturing jobs), you're missing out on the larger picture gains (greater productivity, higher standards of living).
[1]http://www.trivisonno.com/offshoring [2]http://data.bls.gov/timeseries/LNS14000000 [3]http://www.federalreserve.gov/releases/g17/current/
That's not to say the original comment is correct either. It's just that there seems to be many more variables that just one in what determines the unemployment rate.