Based on evidence from the last three decades, polarization in American politics has eliminated landslide presidential victories.

But could Donald J. Trump trigger one again?

His extraordinary White House bid has raised the question. For Hillary Clinton, now leading solidly in the polls, it looms over strategic choices ranging from selection of a running mate to how she contrasts herself with the presumptive Republican nominee.

In theory, Mr. Trump’s message of change, iconoclastic background and stances on issues from taxes to trade create the possibility of appealing broadly across a divided electorate.

In practice, his tempestuous persona, harsh rhetoric and thin preparation have repelled important segments of his own Republican Party as well as Democratic constituencies.