However, it hasn't been known for being particularly accurate.

For what it's worth, High Frequency Economic's Jim O'Sullivan notes that ADP has been getting more accurate in recent months:

...More relevant from a timing perspective, the ADP private payrolls estimate was 198K, above the consensus for the BLS data tomorrow: +170K for comparable private payrolls and +160K in total. Despite the strength in ADP, we have not changed our 130K forecast for the BLS payrolls series, and 140K for private payrolls. Indeed, we had forecast a fairly strong 180K rise in the ADP series. Our forecast for the BLS data allows for a 50K drag from the big Northeast snowstorm that struck just prior to the sample week; such weather effects tend to be much more noticeable in the government data than in the ADP series.