[mookiemookie]

The first recorded use of the expression with its modern meaning is by British politician and orator John Bright, referring to the Reform Bill of 1867, which called for more democratic representation in Parliament, and about which Parliament was singularly apathetic. Trying to rouse Parliament from its apathy on the issue, he said in a speech, would be like trying to flog a dead horse to make it pull a load. The Oxford English Dictionary cites The Globe, 1872, as the earliest verifiable use of flogging a dead horse,

For..twenty minutes..the Premier..might be said to have rehearsed that..lively operation known as flogging a dead horse.

Interesting tidbit I found on Wiki for the "beating a dead horse" article.