Hillary Clinton and Donald Trump launched a two-day campaign whirlwind in battleground states on Sunday in a frantic end to a presidential election race that highlighted shifts in the US electoral map that could decide the outcome on Tuesday.

The Clinton campaign was hoping that a surge in Latino voting would push her over the winning line in Florida, North Carolina and Nevada, while Mr Trump was betting that a heavy turnout of white, working-class voters will allow him to flip previously Democratic strongholds in the industrial midwest.

Mrs Clinton has held a lead in the polls for most of this year and appeared to have more potential paths to the 270 votes needed in the electoral college to win the White House. But surveys have shown a tightening race both nationally and in key swing states over the past two weeks, particularly after the FBI said it was examining new emails related to its investigation of the former secretary of state’s use of a private server.

An ABC/Washington Post poll released on Sunday gave Mrs Clinton a 48-43 lead nationally but found Mr Trump had a 48-45 advantage in an aggregate of five battleground states. A NBC/Wall Street Journal poll on Sunday had her up by four percentage points, while an LA Times poll had Mr Trump up by five.

The narrowness of the race has led to a rewriting of campaign scripts in the final days. The Clinton campaign on Saturday announced a big last-minute push in Michigan, which had previously been seen as a safe state by Democrats and last voted for a Republican in 1988.

Bill Clinton campaigned in the state on Sunday while Mrs Clinton and her two most effective supporters — President Barack Obama and his wife Michelle — will head there on Monday for get-out-the-vote rallies.

At a union hall down the street from two razed auto plants near Lansing, Michigan, Mr Clinton urged a packed hall of union members and college students to work on getting out the vote in this blue collar suburb near the state capitol.

Chris Jackson, a 28 year old lawyer, voted for Bernie Sanders in the state’s primary but now he is a passionate supporter of Mrs Clinton because “we’re fighting for the future of this little guy”, he said, nodding his head at the 11 month old son in his arms.

Ben Frantz, who proudly wears a black shirt embroidered with the medallion of his United Autoworkers local 652, is one of them. “We voted our conscience in the primary, we voted for Bernie, but now the only viable candidate is Hillary Clinton,” he said, without the resignation common in some union areas of Michigan where a higher proportion of members plan to vote for Mr Trump. “In a recent poll, it showed 28 per cent of UAW members identify as Repbulicans,” he said, adding that Mrs Clinton’s campaign was wise to come to Lansing to “get back to basics”.

With many towns and cities that have suffered in a globalised economy, Michigan is the sort of state where Mr Trump’s populist message could resonate, although his campaign had paid little attention to it before the last week. He will visit the state on Sunday evening. Polls show that the Republican candidate is doing well in neighbouring Ohio and Iowa, states which Barack Obama won in 2012 but which also have large populations of white working class voters.

Although public polling has shown Mrs Clinton well ahead in Michigan, chairman of the Republican National Committee Reince Priebus said on Sunday that the state was an “absolute toss-up”. John Podesta, chairman of the Clinton campaign, said: “We feel good about Michigan.”

Mr Trump is making a foray into another Democratic stronghold with a Sunday afternoon rally in Minnesota, which last voted for a Republican presidential candidate in 1972.

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Meanwhile, Democrats have been encouraged by signs of heavy turnout among Hispanic voters in Florida, North Carolina and Nevada, with Mr Trump’s tough campaign rhetoric against Mexican immigrants thought to have motivated a higher number to vote than in previous elections.

If Mr Trump loses Florida, which has 29 electoral college votes, or North Carolina with 15, it will be almost impossible for him to secure the 270 votes needed to win the presidency in the 538-vote electoral college. High Latino turnout could also put the Democrats close to victory in once reliably Republican states such as Arizona and Georgia, with Texas also becoming tighter — a trend that political analysts believe is only likely to continue over the next decade.

The signs of an anti-Trump backlash among Latinos have been particularly strong in Nevada, where Democrats appear to have built up a big lead in early voting. After seeing images of long lines at polling places on Friday evening in Latino neighbourhoods of Las Vegas, the Republican chairman in Nevada, Michael J McDonald, complained on Saturday that polling places had stayed open late so that “a certain group could vote”. “Think this is a free or easy election?” he told a Trump rally in Reno.

Heightened tensions were evident at the same rally when Mr Trump was rushed offstage by his Secret Service bodyguards as police wrestled a man to the ground. The Secret Service later said they had intervened after someone in the crowd shouted “gun”, but that no weapon had been found.

Mrs Clinton has turned to star power in recent days to try to motivate key constituencies — particularly black, millennial and women voters — to get out and vote. After appearing at a campaign concert with pop star Beyoncé in the swing state of Ohio on Friday night, she took to the stage with singer Katy Perry in Philadelphia on Saturday evening. Basketball star LeBron James was due to appear with Mrs Clinton on Sunday in Cleveland.

Mr Trump responded that “I don’t need to bring J-Lo or Jay Z” to draw large crowds, but the lack of star surrogates is forcing the Republican candidate to do much heavy lifting himself in the final days of the campaign. The New York businessman was due to make appearances in five different states on Sunday.

Sunday is an important day for Democrats to mobilise African-American voters, with black churches in states such as Florida, North Carolina and Georgia organising a “souls to the polls” campaign that offers free transport to early polling places from Sunday services.

The final scramble across the battleground states is coming as data show a surge in early voting this year in the 37 states that allow it, with more than 40m people having cast ballots already, according to Michael McDonald, a University of Florida professor.

According to Mr McDonald this year’s early voting has seen an increase in turnout by women and Hispanic voters compared to 2012, trends that are seen to favour Mrs Clinton and Democrats. In states like Nevada the data point to what could be a convincing victory for Mrs Clinton, he said, despite polls showing a tight race to the finish.

“Nevada will be a good test of polls [versus] early vote,” Mr McDonald tweeted on Saturday. “Early vote indicating Clinton win, polls say it is toss-up.”