The unifying principle of the Whig party was?

Answer 1

In its earliest years, the Whig Party was unified solely by its opposition to President Andrew Jackson (leader of the "Democratic" Party).

In fact, the name "Whig" was chosen by party members to identify their opposition to the "tyranny" of "King Andrew" (as they nicknamed him) with that of the British anti-royal Whig Party of the 18th century. (Note that, during the later part of the American Revolution, the Tory Party supported King George III in the war effort, and these were opposed by the Whigs.)

Less cynically, many of the "republican" principles of Whigs in Parliament during the 17th and 18th century were those championed by the founding fathers. The naming of parties to identify the principles they stood for was common early in American history: early supporters of the Constitution were "Federalists"; their opponents (a group organized esp around Jefferson & Madison) adopted the name "Republicans"; Jackson's supporters called themselves "Democrats" or "the Democracy".