"Get With the Tempo" appears on a tape box that simply says, "Larry Kane Lip Synchs," along with several other songs, including: A-440's "When I Get Out," Fever Tree's "Love Makes the Sun Rise" and "The Man Who Paints the Pictures," and Roger Miller's "King of the Road." There is also a commercial for the Young Rascals' first appearance in Houston, which happened in December, 1967, the probable month for this broadcast.
The band here is unknown, but it sure sounds like Neal Ford and the Fanatics with Jon Pereles on lead vocals. "Get With the Tempo" was probably a commercial for the Houston Post's Sunday "Tempo" magazine, hence the lyrics ("you heed the tempo, now read the tempo").
UPDATE: Jon Pereles has heard this and declared that it is not the Fanatics.
Thanks to Craig Malek.