Americans approve of drone warfare by about three to one, for obvious reasons. Drones let us kill the "bad guys" without risking any "good guys" — except when we don't. Killing a couple of hostages turned out to be a bit embarrassing for the Obama administration. Suddenly, people are paying attention again.
Apparently some "faulty intelligence" was to blame. Whoops. Mind you, the CIA is loathe to admit fault. According to the CIA, "collateral damage" occurs less than one per cent of the time. NGOs with personnel in places like Pakistan, Somalia, Yemen, and Afghanistan beg to differ, as do most governments of targeted areas. (Granted, the Pakistanis have been quietly cooperating while noisily complaining, and one of things the CIA really liked about former president Abd Rabbuh Mansur Hadi of Yemen was that he could be counted on to keep his mouth shut.)
The recent "whoops" is unlikely to change any attitudes among the American people, so the politics of drone warfare remains positive for Obama. It also won't make any difference to the prospective civilian casualties living under the drone flights. They'll go right on hating our guts.
Anyway, there may me some rethinking of "signature strikes," where the CIA looks for "patterns" that "indicate" bad guy activity, and wipe out the bad guys without actually knowing who they are. Maybe the Obamites will decide that warfare by assassination works better when you know who you're killing.