  We predict the X-ray background (XRB) expected from the population of quasars
detected by the JWST spectroscopic surveys over the redshift range $z \sim
4-7$. We find that the measured UV emissivities, in combination with a
best-fitting quasar SED template, imply a $\sim 10$ times higher unresolved
X-ray background than constrained by current experiments. We illustrate the
difficulty of simultaneously matching the faint-end of the quasar luminosity
function and the X-ray background constraints. We discuss possible origins and
consequences of this discrepancy.
