Compressibility and viscosity of polymer feedstock are critical to their volumetric flow rate, weld strength, and dimensional accuracy in material extrusion additive manufacturing. In this work, the compressibility and viscosity of an acrylonitrile butadiene styrene (ABS) material is characterized with an instrumented hot end design. Experiments are first performed with a blocked nozzle to characterize the compressibility behavior. The results closely emulate the pressure-volume-temperature (PVT) behavior of a characterized generic ABS. Experiments are then performed with an open nozzle over a range of volumetric flow rates and temperatures. The static pressure data is fit to power-law, Ellis, and Cross viscosity models and the dynamic melt pressure data is then used to jointly fit material constitutive models for compressibility and viscosity. The results suggest that the joint fitting substantially improves the fidelity relative to the separately characterized viscosity and compressibility. The implemented methods support material extrusion process simulation and control including real-time identification of process faults such as (1) limited melting capacity of the hot end, (2) skipping (grinding) of the extruder drive gears, (3) low initial nozzle temperature, (4) varying flow rates associated with the intermeshing gear tooth velocity profile, and (5) delays and reduced melt pressures due to drool prior to extrusion. The ability to monitor the printing process for faults in real time, such as that presented in this work, is critical to born qualified parts. Additionally, these approaches can be used to screen new materials and identify optimal processing conditions that avoid these process faults.