Context. During the past few years, eclipse exoplanet spectroscopy has enabled the detection of H2O, CH4, CO2, and CO in the atmosphere of hot jupiters and neptunes. At the same time,  ~40 likely large terrestrial planets are announced or confirmed. Two of these are transiting, and another is deemed habitable. Therefore the potential for eclipse spectroscopy of terrestrial planets with the James Webb Space Telescope (JWST) has become an active field of study. Aims. We aim to extensively explore the parameter space (type of stars, planet orbital periods, planet types, and instruments/wavelengths) in terms of signal-to-noise ratio (S/N) of the detection of spectroscopic features with the JWST. We also wish to confront the information on the S/N to the likelihood of occurring targets. Methods. We used analytic formula and model data for both the astrophysical scene and the instrument to plot S/N contour maps, while indicating how the S/N scales with the fixed parameters. We systematically compare stellar photon noise-only plots with plots that include detailed instrumental and zodiacal noises. The likelihood of targets is based on both model and catalog star populations of the solar neighborhood. Results. The 9.6 μm ozone band is detectable (S/N = 3) with JWST, for a warm super earth 6.7 pc away, using  ~2% of the 5-year nominal mission time (summing observations, M4 V and lighter host star for primary eclipses, M5 V for secondary). If every star up to this mass limit and distance were to host a habitable planet, there would be statistically a little under one eclipsing case. We also show that detection in transmission of the 2.05 μm CO2 feature on the 6.5   M ⊕  exoplanet GJ 1214 b is feasible with the Hubble Space Telescope (HST). For the low and the high bounds of the likely atmospheric mean molecular weight, just one eclipse or the whole HST yearly visibility window (107 days) is required. Conclusions. It is critical to investigate systematic noises resulting from co-adding hours-long observations separated by tens of days, over a 5 year span. It is also critical to perform a dedicated characterization of the instruments, currently in integration phase. The census of nearby transiting habitable planets must be complete before JWST’s science operations start.