There is no question but that Obama and the Democratic Party have a mandate from the people from this election.
(1) President Obama won the electoral college 332 to 206. He won all the battleground states except for North Carolina.
(2) Obama also won the popular vote.
(3) Not only did Obama win the popular vote, he won an absolute majority of the popular vote (more than 50%).
(4) Obama won more states than Romney did: 26 states to 24.
(5) The GOP will try to say there really was no mandate because the GOP retains control of the House. But the House districts are even less indicative of the popular vote than the electoral college is, because each state is guaranteed a minimum number of representatives, and because of gerrymandered districts. In this election there were actually more votes for Democratic candidates for congress than there were for Republicans! The votes were 53,952,000 for Democrats and 53,402,000 for Republicans. The House of Representatives is really not exactly representative.
So I don’t think there is any doubt but that there was a mandate.