We used atomic force microscopy (AFM) to study the deformation and wetting behavior of large (50-250 m) emulsion droplets upon mechanical loading with a colloidal glass probe. Our droplets were obtained from water-in-oil emulsions. By adding gelatin to the water prior to emulsification, also droplets with a bulk elasticity were prepared. Systematic variations of surfactant and gelatin concentrations were made, to investigate their effect on the deformation and wetting behavior of the droplets and to identify the contributions of interfacial tension, bulk elasticity, and expelled water. The AFM experiments were performed in force-distance mode and showed on approach a repulsive regime which in many cases was terminated by a jump-in of the probe. In the case of pure water (i.e. gelatin-free) droplets, the repulsive part of the curve showed a good linearity, thus allowing the extraction of an effective droplet spring constant. This quantity was found to decrease on raising the surfactant concentration from below the critical micelle concentration (cmc) to well above the cmc, and its numerical values were found to correspond remarkably well to literature values for the interfacial tension. Our findings indicate that, on gelatin increase inside the droplets, the bulk elasticity gradually becomes dominant and the droplets' stiffness does not depend anymore on surfactant concentration. Also the stability of the droplet interface against wetting, as measured by the force at which the jump-in instability occurs, was enhanced by gelatin. For gelatin concentrations of 15 wt %, the droplets were found to behave like purely elastic bodies. Both gelatin and surfactant contribute positively to the stability against interface breakup.