Observing the motion of electrons on their natural nanometer length and femtosecond time scales is a fundamental goal of and an open challenge for contemporary ultrafast science. At present, optical techniques and electron microscopy mostly provide either ultrahigh temporal or spatial resolution, and microscopy techniques with combined space-time resolution require further development. In this study, we create an ultrafast electron source via plasmon nanofocusing on a sharp gold taper and implement this source in an ultrafast point-projection electron microscope. This source is used in an optical pump—electron probe experiment to study ultrafast photoemissions from a nanometer-sized plasmonic antenna. We probe the real space motion of the photoemitted electrons with a 20-nm spatial resolution and a 25-fs time resolution and reveal the deflection of probe electrons by residual holes in the metal. This is a step toward time-resolved microscopy of electronic motion in nanostructures.