Presidential debates matter in American politics. And the one that takes place on Tuesday night between Donald Trump and Kamala Harris – their only currently scheduled face-off – may matter more than most.

Joe Biden’s poor performance in the first presidential debate in late June created a firestorm of pressure within the Democratic Party that ultimately forced him to abandon his re-election campaign.

Even though Kamala Harris has been vice-president for more than three years and a candidate for president for seven weeks, she is still a relative unknown for many Americans. In a recent New York Times survey, 28% of likely November voters said that they needed to know more about the Californian.

That poll showed the race a statistical dead heat – a finding most recent surveys have also indicated, both nationally and in key battleground states. The 2024 presidential campaign has been full of historic tumult, but the American electorate is still sharply – and narrowly - divided.

That underscores the importance of Tuesday night’s debate, where even small shifts in the mood of the electorate could be the difference between victory and defeat for the candidates.

For Ms Harris, the showdown in Philadelphia provides an opportunity for her to flesh out the details before an audience of tens of millions – although she will have to do so while under rhetorical fire from her Republican opponent.

This opportunity is not without risks, however, as Ms Harris could define herself – and her positions – in ways that damage her electoral prospects. She has struggled in the past with answering pointed questions under pressure, and her reluctance to sit for media interviews in the opening weeks of her campaign has denied her the opportunity to hone her linguistic chops.

Although she has tried to present herself as the change candidate in this election, the moderators – and the former president – are likely to press her to defend the Biden administration’s record, particularly on areas where polls show Democrats are weak, such as border security and inflation.

She will also have to explain why she has renounced some of the more liberal policies she embraced during her unsuccessful bid for the 2020 Democratic presidential nomination. She recently has walked back her positions on a fracking ban, decriminalising border crossing and nationalising health insurance, among others.

She has explained these changes as ones made to reflect new circumstances – but they may be viewed by some voters as moves born of political expediency.

For Trump, the debate presents an opportunity to wrest back the initiative in this campaign after a month where the Democrats – with their new nominee and high-energy convention – dominated political headlines. He has a history of thriving in the spotlight and setting the terms of political conversation that keeps his opponents off-balance and his issues – notably on immigration and trade, where his positions have broad popular support – at the forefront of political discussion.

The former president has his own potential pitfalls on Tuesday, however. His uneven performance during his June debate with Mr Biden drew little scrutiny because of his opponent’s sometimes catastrophic verbal miscues. Ms Harris is sure to present a more nimble opponent, and his answers will have to be sharper.

During a New York economic forum last week, he was unable to offer a clear explanation for his childcare policies. Such verbal meandering during the debate will provide Democrats with a wealth of campaign fodder.

Trump must also tread carefully when sparring with the vice-president – only the second woman presidential nominee and the first of colour. If he comes across as domineering or belittling, he could further damage his already weak support among female voters.

The two candidates have used markedly different ways of preparing for Tuesday night’s event. The vice-president – and former prosecutor - has been in Pittsburgh, a few hours' drive east of Philadelphia, holding mock debates and reviewing her policy proposals. The move also allowed her to campaign and benefit from some local media coverage in the largest and most crucial battleground state of Pennsylvania.

Trump - who has participated in presidential debates in each of the past three elections - has held more informal sessions, including reviewing his positions on key issues. Last week, he participated in a town hall forum hosted by conservative cable network Fox News.

Tuesday, then, is set to be a contrast of styles as well as political views.

Although election day won’t arrive until November, early voting is set to begin this month in some key battleground states – including in pivotal Pennsylvania.

So while this debate could help set the political environment for the last two months of the 2024 presidential race, it also will be the last chance for the two candidates to reach some voters in states where every ballot matters.

North America correspondent Anthony Zurcher makes sense of the race for the White House in his weekly US Election Unspun newsletter. Readers in the UK can sign up here. Those outside the UK can sign up here.