Viscometric functions for a dilute polymer solution, undergoing steady simple shear flow, are predicted using a modified version of the Rouse model. The presence of excluded volume interactions between different parts of a polymer chain, which is not taken into account in the original Rouse model, is incorporated into the present model with the help of a narrow Gaussian repulsive potential, which acts pairwise between the beads of the Rouse chain. Exact results are obtained numerically with the help of Brownian dynamics simulations, since the analytical tractability of the Rouse model is lost due to the modification. The presence of excluded volume effects is shown to cause the viscosity and the first normal stress difference to decrease with increasing shear rate-a feature not predicted by the Rouse model, though commonly observed experimentally. The exact simulation results are used to assess the quality of an approximate solution, obtained by assuming that the nonequilibrium distribution function is Gaussian. The Gaussian approximation is found to be accurate within a certain range of parameter values. By extrapolating data acquired for chains of finite length to the infinite chain length limit, it is shown that the predictions of the Gaussian approximation become universal in this limit, independent of model parameters. The predicted universal dependence of the normalized viscosity, and the normalized first normal stress difference, on a characteristic nondimensional shear rate, is shown to be well represented by the Carreau-Yasuda model.