WASHINGTON—Donald Trump won the White House in large part by changing the mix of voters who make up the Republican Party. Now, as he faces the threat of impeachment, the party base he helped to create is proving to be his most important barrier to removal from office.

Mr. Trump accelerated the movement of working-class voters into the Republican Party, creating a GOP that now represents more middle- and lower-income Americans, a Wall Street Journal analysis shows. He has reframed much of the Republican agenda to appeal to...