We calculate the one-electron spectral function of the attractive-U Hubbard model in two dimensions. We work in the intermediate coupling and low-density regime and evaluate analytically the self energy. The results are obtained in a framework based on the self-consistent T-matrix approximation. We also calculate the chemical potential of the bound pairs as a function of temperature. On the basis of this calculation we analyze the low-temperature resistivity and specific heat in the normal state of this system. We compare our results with recent beautiful tunneling experiments in the underdoped regime of HTSC-materials.