(Sorry, don't know why the thumbnail's not displaying, but the video does work and is well worth your time!)
As the good folks at PCL LinkDump noted, this clip is "From the 1966 movie STING OF DEATH, the greatest movie ever made featuring a half man, half jellyfish villain. If you enjoy close-up shots of girls butts in tight pants, then this movie is for you!" And, yes, that's Neil Sedaka doing the singing.
You should really click on over to their site, where they've also fixed us up with some fantastic screen captures. Tip of the cap to Thom Tex Edwards for bringing this to my attention.