The mechanical and viscoelastic responses of poly(ethyl methacrylate) (PEMA) ultrathin films over thicknesses ranging from 21 to 112 nm have been studied using a nanobubble inflation method. The stress-strain response of the PEMA thin films shows a rubbery stiffening as the film thickness decreases, and the present results are combined with prior measurements of the rubbery stiffening index S for multiple polymers. We find that S is linearly correlated with the dynamic fragility index m. The results are also consistent with expectation from Ngai et al.'s [ J. Polym. Sci., Part B: Polym. Phys. 2013, 51 (3) ] recent proposition based on his coupling model but do not seem to correlate with the molecular composite concept proposed by Page et al. [ Nano Lett. 2014, 14 (5) ] as a means to explain the dependence of the rubbery stiffening on chemical structure of the polymer. In addition, we observe a reduction in glass transition temperature of as much as 15.7 K for PEMA films of 21 nm thickness.