As Republicans begin choosing a general-election candidate here Tuesday night, one question could shape the destiny of the eventual winner: Will the nominee define the party, or will the party define the nominee?

Successful presidential nominees often have helped redefine their parties. Ronald Reagan’s conservatism changed the Republican Party when he became the GOP nominee in 1980. Bill Clinton portrayed himself as a New Democrat, which proved a key to his victory in 1992. In his 2000 campaign, George W. Bush used the term “compassionate conservative” to put distance between himself and the congressional wing of his party that had been defined by Newt Gingrich.