High electron density effects on photoyield and electron energy distributions have become important in several electron spectroscopies and in electron microscopy since the availability of high-intensity photon and electron sources. In this work we show that such effects also lead to limitations in voltage sensitivity and time resolution in photoemission and electron-beam sampling measurements of voltage signals if picosecond time resolution is required. The influence of high electron densities in picosecond pulses for these methods is analyzed theoretically and compared with experimental results in photoemission sampling. It is shown that the space-charge limitation to the number of electrons per pulse which can be emitted from a sample and the energy broadening of the pulse owing to the Coulomb repulsion between the electrons impose significant limitations on the voltage sensitivity of photoemission sampling and of electron-beam sampling with a pulsed high-intensity cathode. Also the time resolution is degraded by the space-charge limitation in photoemission sampling and by the Coulomb broadening in electron-beam sampling. The theoretical analysis of these effects is done within a simple electrostatic model for the space-charge and Coulomb effect and a derivation of a generalized brightness condition from the Liouville theorem of statistical physics which includes the high electron density effects.