Hillary Clinton is rushing to Detroit on Friday amid unexpected nervousness inside her campaign that Michigan, a state they thought they could count on, might fall to Donald Trump.

The decision to include Michigan in her schedule in the last few days of the election is another sign that the race for president is tightening in unpredictable ways, with polls showing Mr Trump still at a disadvantage but nonetheless enjoying what could be a final spurt of momentum.

Snatching at least one blue-leaning state on election day could significantly widen Mr Trump’s options for reaching the magic 270 votes in the electoral college. That said, everything else would have to go right for him too, including bagging Ohio, Florida and North Carolina.

On Thursday, both candidates were pouring their energies into North Carolina. Ms Clinton was due to appear at a rally in the state alongside Pharell Williams, the music star, in the hope that his appearance would boost African American turnout. Early voting data has suggested that black support for the Democrats is lagging behind where it was for Barack Obama four years ago.

The furious campaigning by both sides comes as new national polls show the Democrat candidate enjoying only the slightest of edges over her Republican foe. The narrowing of the race comes nearly a week after the FBI revealed it had uncovered a huge new trove of emails that it said could end up having a bearing on its previously closed probe into her private email server.

Ms Clinton led by 3 percentage points among 1,333 registered voters in a fresh New York Times/CBS poll taken between 28 October and 1 November. The FBI dropped the email bomb on 28 October. The survey showed Ms Clinton with 45 per cent support compared to 42 per cent for Mr Trump.

When it comes to the vital swing states, there is no space for complacency for either side. A RealClearPolitics average of polls in Florida, which carries 29 electoral votes, put Trump 0.7 point ahead of Clinton. In North Carolina, it had the race with both candidates at 46 per cent.

Both campaigns know that a loss for Mr Trump in Florida alone would essentially block any path he might have to victory, thus ensuring a blizzard of last-minute campaigning and television advertising up and down the Sunshine State before election day on Tuesday. President Barack Obama flew to Miami on Thursday in the south of the state where Democrat support is strong.

“All of the progress we’ve made goes out the window if we don’t win this election,” Mr Obama declared, imploring the crowd to vote Ms Clinton and preclude a Trump presidency.

Yet Ms Clinton is also being forced to make last-minute stops elsewhere. On Wednesday night she drew 15,000 supporters – one of her biggest crowds yet – to a rally in Arizona, a state that has shown some signs of flipping from Republican to Democrat.

But while the Arizona appearance suggested some lingering confidence in her campaign, suggestions of just a week ago that she could achieve a landslide have now largely faded away. And the new reality that Mr Trump is now threatening her to a degree not before anticipated is evidenced by the sudden attention being paid to Michigan.

On Wednesday night Bill Clinton made an unannounced visit to the Detroit area where he met with black leaders and pastors, again in an effort to energise the African American vote for his wife. Meanwhile one pro-Clinton group said it was spending $1m on additional advertising in Michigan and another $1m in Colorado, where her lead may be even more tenuous.

Her supporters have similarly been redirecting resources to Wisconsin and Minnesota, two other upper midwestern states where the Trump campaign believes it could blow holes in her firewall.

As election day approaches, there is also concern that the polling may not fully reflect Trump support. That view was rehearsed on CNN by Nigel Farage speaking of what he said was the disjuncture of polling and actual results during the Brexit referendum. “On the day of the vote, there was an opinion poll that put us 10 points behind, but we won,” he told the news network.

“Modern polling companies cannot get to non-voters who are re-entering the system,” the interim UKIP leader added. “The question is, is Trump reaching non-voters? I’m told that new registration of voters is quite high. It could be that Hillary’s ahead, but maybe by not so much.”

The Clinton campaign remains haunted by the FBI’s actitivites. In addition to it revealing the existence of the new emails, the airwaves on Thursday crackled with reports that the agency spent part of this year jousting with the Justice Department over whether to launch an investigation into the Clinton Foundation and allegations of favours being given to donors.

As it grappled this summer with possibly issuing subpoenas in the case, the FBI was drawing in part on content from a highly critical book about the Clinton family, Clinton Cash: The Untold Story of How and Why Foreign Governments and Businesses Helped Make Bill and Hillary Rich, by conservative author Peter Schweizer.

According to The Wall Street Journal, agents with the FBI also became convinced that secret recordings of a suspect speaking about the foundation also gave them grounds to open an official probe but the effort was quashed by prosecutors in the Justice Department who did not share their assessment of what the tapes contained.

In the final days, Ms Clinton is doubling down on her message that Mr Trump has disqualified himself to be president.

“Imagine having a president who demeans women, mocks the disabled, insults Latinos, African Americans, the disabled, POWs, who pits people against each other,” the Democratic presidential nominee asked the giant crowd on the campus of Arizona State University on Wednesday night.