I think that to deny that a Dem President who receives a majority of the popular vote and a majority in the electoral college has received a mandate is a virtually impossible argument to make on the numbers.
The better way to argue that Obama did not receive a mandate for a particular policy or policies would be to show, if possible, that he did not campaign on such policies and therefore the people who voted for him did not give him a mandate to bring in such policies.
This would need to be addressed on an issue by issue basis.