We present an experimental study on the surface rheology of ultrathin films of poly(tert-butylacrylate) (PTBA) and poly(tert-butylmethacrylate) (PTBMA) for which steric hindrance imposed by the methyl group leads to a large intrinsic rigidity of the polymer chain. Whilst PTBA films show weak temperature dependence, PTBMA films undergo a solid-liquid transition at a temperature well below T(g), the glass transition temperature of the bulk polymer. The peculiar behaviour observed for the shear moduli beyond the fluid-solid transition is similar to that observed recently with dispersions of soft colloidal spheres [D. A. Sessoms, et al., Phil. Trans. R. Soc. A, 2009, 367, 5013-5032], where, upon cooling, the system undergoes first a glass transition, followed by a jamming transition. The transition that we observe in PTBMA films could be similar or, alternatively, could be analogous to the glass transition of the bulk polymer.