Welcome back to your weekly update on US politics, where North America bureau chief Jade Macmillan catches you up on the biggest developments in America as we hurtle towards election day in November.

Local government jobs don't get much more high profile than the one held by the person elected to lead New York City.

So when the mayor of America's biggest metropolis was charged with taking illegal campaign contributions from foreign nationals this week, the political shock waves were felt far beyond Manhattan.

Democrat Eric Adams has been accused of five federal offences, including bribery and wire fraud.

Prosecutors allege he abused his position by soliciting the campaign donations, and by accepting bribes from Turkish nationals in the form of luxury travel and accommodation.

In exchange, he's accused of pressuring the city's fire department to allow the opening of a new Turkish consular building, without the need to pass a safety inspection.

The mayor insists he's innocent of the charges and won't be stepping down from his position.

He's also hit out at federal prosecutors, appearing to take a leaf out of former US president Donald Trump's playbook by suggesting he's being targeted for political reasons — in his case, for criticising the Biden administration over its immigration policies.

"I always knew that if I stood my ground for all of you, that I would be a target, and a target I became," he said in a video message.

"Despite our pleas, when the federal government did nothing as its broken immigration policies overloaded our shelter system with no relief, I put the people of New York before party and politics."

Adams fell out with President Joe Biden, a fellow Democrat, amid accusations the federal government had not provided New York with enough support to deal with an increase in the number of asylum seekers arriving in the city.

The White House would not comment on the mayor's indictment, other than to insist the Department of Justice (DOJ) was not influenced by political factors.

"The president was clear, even when he was running in 2020, that he was going to make sure that DOJ is independent," press secretary Karine Jean-Pierre told reporters.

"DOJ is handling this case independently. I'm not going to go beyond that."

New York is considered reliably safe for Democrats in the presidential race, meaning the mayor's legal woes are not expected to affect Vice-President Kamala Harris's chances of winning there.

But the state could play an important role in deciding which party takes control of the House of Representatives after the election, and the ability of the new president to implement their legislative agenda.

Several Democratic candidates vying for House seats are already calling on Adams to resign. But the state's Democratic Governor, Kathy Hochul, who has the power to sack him, has indicated she's still weighing her options.

Trump, meanwhile, used the saga to try to further his own argument that he'd also been the target of political prosecutions.

"I wish him luck," he said of the mayor.

Trouble for Trump in North Carolina?

Trump is facing a more difficult political situation in North Carolina, where the Republican candidate for governor has become mired in scandal.

Mark Robinson currently serves as lieutenant governor — the state's second highest elected official — and was endorsed by the former president in his bid for the top job.

Trump had previously been full of praise for the 56-year-old, describing him as "unbelievable" and "one of the great stars of the party".

But Robinson's campaign has been in crisis mode since CNN reported allegations that he'd made offensive and inflammatory comments on a pornography website's message board a decade prior, including one in which he allegedly referred to himself as a "black Nazi".

Robinson has denied the claims, and the ABC has not independently verified them.

Kamala Harris's team seized on the news though, releasing a new ad highlighting the former president's previous support for the lieutenant governor.

And when Trump held a rally in North Carolina in the aftermath of the story being published, Robinson did not make an appearance or get a mention.

Democrats haven't won the state in a presidential election since Barack Obama flipped it in 2008. 

But Trump claimed victory in North Carolina with only a very slim margin in 2020, and Kamala Harris's team is hopeful the vice-president could pick it up.

The governor's race does not technically affect the presidential contest. Voters in North Carolina are free to choose candidates from different parties for each of the positions being decided.

The risk for Trump is that Harris's effort to link him to yet more controversy succeeds in swaying people against him in what's expected to be a very tight race.

In case you missed it: The little blue dot at the centre of a big fight

Less than six weeks out from election day, the two major party candidates are focusing most of their time and money on the seven 'swing states' considered up for grabs by either side.

The aforementioned North Carolina is one of them, along with Pennsylvania, Michigan, Wisconsin, Georgia, Arizona and Nevada.

But a voting peculiarity has made the Midwestern state of Nebraska also one to watch.

Most states have a 'winner takes all' approach under the electoral college system that decides the presidency.

If a candidate receives the majority of ballots cast in Pennsylvania, for example, they pick up all of the state's 19 electoral college votes.

Nebraska's process for allocating its five electoral college votes is more complicated.

The candidate with the most support overall gets two votes, while the remaining three are awarded based on the results in each of its congressional districts.

Trump won four of Nebraska's five votes in 2020, but lost the district which takes in the more liberal-leaning city of Omaha to Biden.

Depending on how all of the swing states end up falling, there's a scenario in which the so-called "blue dot" could get Harris to the magic number of 270 votes needed to enter the White House.

Republicans have recently tried to change the voting rules in Nebraska to a winner takes all model, without success.

It means the small blue dot in the middle of the country could be front and centre come November 5.