The Bureau of Labor Statistics' key economic releases would be postponed in the event of a government shutdown, per the Department of Labor's plan for such an event - PDF link. 
- "BLS will suspend all operations. Economic data that are scheduled to be released during the lapse will not be released. All active data collection activities for BLS surveys will cease. The BLS website will not be updated with new content or restored in the event of a technical failure during a lapse."
- Furthermore: "The releases of economic data will likely be delayed if a lapse is prolonged....A reduction in quality of data collected might impact the quality of future estimates produced."
- This was largely expected - at least for the key BLS data points in the next couple of weeks, namely the September employment report (due out this Friday Oct 3) and the September CPI report (due out Weds Oct 15)), as well as PPI (Oct 16). The shutdown would begin at midnight on Wednesday October 1 unless agreement is reached on government funding. 
- It was unclear whether the weekly jobless claims reports would still be published, however, since while they are compiled and released by the BLS, they use state-by-state data and were published in 2013 during the last full federal government shutdown.