The debate on Tuesday night stands to be the most important night in Vice President Kamala Harris’s political career. It will offer her her biggest audience yet as the country tries to learn more about what kind of president she would make.

Former President Donald J. Trump enters the debate hoping to turn the page on a tough summer. Ms. Harris has closed the polling gap with him since she replaced President Biden as the Democratic Party’s nominee. Tuesday may be one of Mr. Trump’s best shots to reverse that momentum before Americans begin early voting.

Ms. Harris’s aides and supporters want her to goad the former president into delivering incoherent rants. The Trump team wants him to turn the conversation back to three areas they consider winning terrain: the economy, immigration and global chaos.

With no other debates scheduled between Ms. Harris and Mr. Trump, the face-off figures to be one of the highest-stakes 90 minutes in American politics in generations.