The election, triggered by a party colleague resigning his seat, has brought unusual attention to the former coalmining area near Manchester as its result will determine the shape of an inevitable challenge to the deeply unpopular Keir Starmer.
If Burnham defeats the candidate for Reform UK, Brexit advocate Nigel Farage's populist party, his victory on Thursday will fire the starting gun on a race to replace Starmer as leader of the Labour Party, a contest that could give Britain its seventh prime minister in just more than a decade.
Starmer himself has pledged to fight on.
Burnham, 56, made two unsuccessful bids to become Labour leader, in 2010 and 2015.
He has mostly tried to play down his leadership ambitions by casting the by-election as a fight to improve the life chances of people in the area, close to where he now lives and where his three children went to school.
But more attention has focused on his hints of how he might govern Britain, leading to accusations from other candidates that, to him, the poll is just a stepping stone to winning national power.
"Change is coming, but the question tonight is 'what kind of change?'" Burnham said in a speech to party supporters, also broadcast on X, late on Wednesday.
"A vote for me is a vote to end 40 years of trickle-down economics that didn't trickle down much at all to people here."
After flooding Makerfield with senior ministers and dozens of MPs, Labour is nervously confident that Burnham can defeat Reform's candidate, Robert Kenyon, a self-employed plumber who is also from the area.
Polls put Burnham ahead with Reform close behind, its share of the vote dented by a new right-wing party called Restore Britain.
Results are expected in the early hours of Friday.
If Burnham wins, he has made clear he would run in any leadership race against the prime minister, although he might not move immediately.
Another leadership rival, former health minister Wes Streeting, says he is prepared to trigger a challenge if Starmer does not step down as Streeting has urged.
Starmer, 63, has repeatedly said he will contest any leadership bid, saying he has "always battled against the odds" by taking a Labour Party that suffered its worst defeat for 84 years in 2019 to a landslide victory in 2024.
But several senior Labour MPs say Starmer could be persuaded to hand the reins to Burnham, who appears to command significant support among Labour members of parliament, to prevent a months-long leadership contest that could further alienate voters before a national election due in 2029.
Burnham could then offer Streeting a high-profile cabinet job in return for declining to trigger a contest for the leadership, Labour MPs said.
One senior MP said the party's standing could only suffer from a likely three-month leadership campaign over the summer, and that its members of parliament were likely to prioritise a quick, clean resolution.
