I ran a couple of tests on our index. We have daily indexes with a somewhat similar load as you. Hardware and index structure can always make a difference though so the results may be meaningless.
Doing a cardinality on a string field across 125 million records took 5 seconds. Doing it across 760 million records took 16 seconds. We have less distinct records than you do though, the second test only had 1.6 million distinct values. We also have other indexes and searching going on that could have affected the performance.