The consensus seems to be that SPQR means Senatus Populusque Romanus, but there is also the theory that SPQR did not mean Senatus Populusque Romanus.
It could also may have been Senatus Populus Quirites Romani.
I've read this in the entry for Quirites in the dictionary Langenscheidt Großes Schulwörterbuch Lateinisch-Deutsch which I unfortunately don't have access to right now.
