It means they will oxidize the oil. On average, oil has two hydrogen atoms to one carbon atom. CH2 + 1.5O2 => CO2 + H2O, so consuming 14 grams of oil requires 48 grams of oxygen. So, that means that consuming e.g. 50 million gallons of oil requires 150,000 metric tons of oxygen.
The oxygen concentration of the sea is around 7 mg/kg. So, 150,000 metric tons of oxygen is all the oxygen in 22 cubic kilometers of seawater. 22 cubic kilometers in the Gulf of Mexico is approximately one drop in a 5 gallon bucket.
Bottom line: there is plenty of oxygen, even at depth, to oxidize all the oil spilled.