We start with Fox News Poll: Majority supports use of drones (by Dana Blanton, March 04, 2013) (interviews conducted 25-27 Feb 2013, before Rand Paul's filibuster) (poll internals):

Do you approve or disapprove of the United States using unmanned aircraft called drones:

To kill a suspected terrorist in a foreign country?

Approve 74%
Disapprove 22
(Don’t know) 4

To kill a suspected terrorist in a foreign country if the suspect is a U.S. citizen?

Approve 60%
Disapprove 36
(Don’t know) 5

To kill a suspected foreign terrorist on U.S. soil?

Approve 56%
Disapprove 40
(Don’t know) 4

To kill a suspected terrorist who is a U.S. citizen on U.S. soil?

Approve 45%
Disapprove 50
(Don’t know) 5
However, three weeks later, we have Gallup with In U.S., 65% Support Drone Attacks on Terrorists Abroad - Less than half of Americans are closely following news on drones (by Alyssa Brown and Frank Newport, March 25, 2013) (after Rand Paul filibuster) (poll internals):



(much more in article).

Two factors are probably at play here: (1) The legislative hearings re: drones, including the Rand Paul filibuster; and (2) The methodological variation in the two polls - Gallup ran two separate polls.

Regards

Mike