efficient authentication with broadcast encryption?
The answer to your question is yes this is possible, but if we don't use assymetric cryptography, we need an alternate source of assymetry. One option is using time-delayed schemes. In such schemes, the key for the MAC is not initially disclosed, but only after some time interval. 

See here for TESLA that accomplishes this. TESLA has a drawback in that it requires an initial digital signature to send the initial parameters. A second variation of TESLA, uTESLA  achieves this without digital signatures.