There is a great deal of room for questioning whether Bush truly has a mandate entering his second term. He won the Electoral College only 286-252 (if his Iowa lead holds), won three states by miniscule margins (Iowa, New Mexico, Nevada; Kerry won Wisconsin in a similarly close result), and certainly did not claim a margin of victory anywhere near the triumphs that Bill Clinton recorded (370-168 in '92, 379-159 in '96).
But even the NY Times concedes that Bush has a mandate to some degree. How?
First, Bush had coat-tails -- he pulled Republican Senators into office with him in Georgia, Florida, South Dakota and the Carolinas in formerly Democratically held Senate seats. He helped the Republicans increase their House majority too. Thus, for the first time since 1936 the President is re-elected, his party rules both houses of Congress and those majorities increased. Clinton had an antagonistic Congress that flipped from Democrat majorities to the first majority Republican House in 40+ years on his watch.
Second, Bush is the first majority President since George H. W. Bush in 1988. That means he is the first presidential candidate to win a majority of the popular vote since his old man did it. Clinton never did. The last Democrat to win a majority of the popular vote was LBJ.
Third, aside from the large Kerry majorities in populous New York, Massachusetts and California, Bush did dominate the popular vote. This country is not quite so polarized as pundits would like to believe -- just look at the Bush dominance in the county-by-county map posted by Whiskey and referenced in my post below. In New Jersey, Pennsylvania, Michigan, and even California, Bush closed the gap between his deficit to Gore in 2000 and his deficit to Kerry this year.
Bush is a polarizing figure for a number of reasons, few of which should be attributable to Bush the man. But his victory does enhance the balance of power tilt toward Republicans and could help the 2008 Republican nominee who will not be saddled with Bush's high negatives.