There are a number of fundamental approaches that have been taken to this trendie, ADP being the most significant (in terms of effort, long-standing and sheer number-crunching) but none have shown any consistently demonstrable success in showing (a) which way the data will go and (b) how the market will react/not react to that data, or more importantly, to the difference between the estimate and the actual. Bear in mind the US needs 150,000 new jobs a month to stay static.
You could always carry out TA on the NFP data itself…or…