Usually, the storm drainage and the sewage system are kept diligently separate. That's because the water treatment requirements are hugely different. (It's why folks are told never to dump waste oil in the street, too.) Since the sewage systems have essentially been "drained" into the floodwaters, the opportunity to treat the waste is nonexistent. I wonder if the pumps are separate ... with separate pumps for the sewers into waste treatment facilities. Maybe they could get the water treatment up and running sooner and run just the sewage pumps. It'd sure take longer, though.
On edit: After reading the link you kindly provided, it's clear the Sewerage System has a far greater capacity than the Drainage System.
New Orleans' sanitary sewer system consists of 1450 miles of lateral and trunk sewers. The system requires 82 electrically operated pumping and lift stations. All but three stations are automatically operated with no attendance other than maintenance checks. Sewer Stations A,D (both on the Eastbank) and C (on Westbank) are large attended stations. The pump stations transfer sewage to two treatment plants operated by a private company under contract to the S&WB. The larger sewage treatment plant is on the Eastbank and the smaller plant is on the Westbank in Algiers.
The need to get the treatment plants up and running as soon as possible is dire, imho. (It's my understanding that "Westbank" means the Mississippi River. No? Or are they the opposing banks of the Mississippi itself and both, therefore, on the Mississippi?)