You can stiff the president on a policy issue and defy him on a political one, but who can turn down an invitation to the White House? Using one of the world’s most famous private residences as bait, President Barack Obama and first lady Michelle Obama are unleashing a bipartisan charm offensive and exploiting every square inch of their new home to make friends and influence rivals. The social calendar suggests a return to the days of Camelot. Since moving into their new digs, the first couple has hosted a half-dozen gatherings — from bipartisan cocktail receptions to a public...