Understanding and optimizing transport between metal contacts and graphene is one of the foremost challenges for graphene devices. In this letter, we present the first results on the effects of reducing contact dimensions to the nanoscale in single-layer graphene transistors. Using noninvasive voltage probes to the graphene channel, the contact resistance was extracted and observed to increase dramatically at contact lengths below 200 nm. Also affected was the extrinsic transconductance, reducing by more than 70% when scaling the contacts from 200 to 50 nm. No significant change in performance per unit width was observed when reducing the contact/device width from 500 to 80 nm. These results provide key insights into the ultimate scalability of graphene transistors, particularly when considering them for a densely integrated technology.