LAS VEGAS (NYTIMES) - The Las Vegas Police had a quandary. They were on high alert for election-related threats, but when long lines of voters began snaking down streets and around parking lots two weeks ago, they feared that stationing patrol cars outside polling stations might drive people away.

"How do you make people feel safe in that environment without creating an overt police presence - that is a challenge for all police departments," said Mr Andrew Walsh, deputy chief in the Homeland Security division of the Las Vegas Metropolitan Police Department. They decided that frequent but random patrols to look for potential trouble was the better choice.

Striking that balance is at the root of many of the challenges facing law enforcement agencies nationwide as they prepare for an election rife with uncertainties.

The largest departments have run practice drills on scenarios including violent clashes between supporters of President Donald Trump and Mr Joe Biden, the sudden appearance of an armed paramilitary group, a cyberattack or a bomb.

"This is such a polarised environment and a lot of people are angry," said Mr John Cohen, a former Homeland Security counter-terrorism coordinator with 34 years experience in law enforcement. "I have never seen a threat environment as dynamic, complex and dangerous as the one we are in right now."

Police in Las Vegas - like their counterparts in New York, Detroit, Chicago, Houston, Los Angeles and in other cities all across the country - are grappling with deploying significantly more officers to counteract any disturbances without scaring voters away.

So far, cities have stayed mostly quiet. And law enforcement officials like Mr John Miller, the deputy commissioner of Intelligence and Counterterrorism for the New York Police Department, have stressed that no "parade of terribles" has materialised so far.

As Election Day nears, many senior law enforcement and other officials have attempted to inject calm while simultaneously warning of dire consequences for those who would disrupt voting.

The attorney-general in Ohio, Mr Dave Yost, a Republican, warned that nobody would be allowed to break the law by blocking people from voting. "Hands off the polling places, hands off the vote," he said in a video statement.

At the same time, many jurisdictions have sought to educate both the public and law enforcement of what is permissible at the polls.

Mr Larry Krasner, the Democratic district attorney in Philadelphia, issued a six-page memo on the law to the police, noting for example that anyone can face five years in jail for a misdemeanor if they "unlawfully strike, wound or commit an assault and battery upon the person of any elector" in or near a polling place.

His office will deploy a task force of 80 prosecutors and county detectives on Election Day, up from 60 for previous presidential races. Mr Krasner warned that anyone "dressed up as G.I. Joe" and trying to intimidate voters would face trial in Philadelphia.

Battleground election states like Pennsylvania, with a history of both leftist activists and armed, far-right groups, are being watched closely for potential violence. So too are Michigan, Wisconsin, Florida, Georgia and Oregon. Nationwide, five protesters have been shot dead during clashes in recent months.

Much attention is focused on Michigan given the early October arrest of 14 men linked to a paramilitary group and accused of violent plots, including kidnapping Governor Gretchen Whitmer over her coronavirus lockdown orders.

Elections officials in some cities there have trained poll workers to deal with disruptive people at the polls or aggressive challengers at absentee vote counting boards.

In the city of Pontiac, Mr Garland Doyle, the city clerk, said every polling station would post a worker outdoors to monitor activity.

Mr James Craig, the Detroit police chief, said the department would be out "en masse," not at polling stations but nearby, and Ms Dana Nessel, the state attorney-general, said that would be true across Michigan.

"There won't be law enforcement at the polls, but they'll be ready to go if there are bad actors who are engaging in intimidation or threatening behaviour and dispersing people if they're causing trouble," she said.

Many police officials and extremism experts said that they were more worried about the period after Nov 3, especially if no clear winner emerges.

Some adherents of the far right view the election as an opportunity to incite violence and accelerate their goal of a civil war. "For the far right this moment is really a flashpoint," said Ms Cassie Miller, a senior research analyst on extremist groups for the Southern Poverty Law Centre.

The post-election period often pops up on forums frequented by paramilitary types. "Past Nov 3 the gloves come off," one person wrote recently on such a forum.

A few leaders of larger paramilitary groups with chapters sprinkled across the country have said their members will deploy on Election Day, but the track record on members actually showing up for planned events is mixed.

If any armed paramilitary groups mobilise, experts said, it will likely be an ad hoc, local situation, much like the men who appeared within hours in Kenosha, Wisconsin, in late August after a resident issued a call to arms on Facebook. Much hinges on President Donald Trump himself, they said.

"If President Trump or the right-wing media begin putting out the message that there is voter fraud or something irregular, that could be something that could bring people out to polling places pretty rapidly," Ms Miller said.

National Guard units were also being called out in various states, including New Jersey, Wisconsin and Texas.

Officials in the first two said the dearth of poll-station volunteers amid the pandemic meant a few hundred troops in civilian clothing would be needed to help count absentee ballots and other poll activities.

For Election Day, New Jersey staged its first statewide practice run combining the efforts of law enforcement and election officials from each of 21 counties more than a year ago, said Mr Jared Maples, director of the New Jersey Office of Homeland Security and Preparedness.

The office ramped up training to respond to cyberattacks on polling places from either foreign or domestic sources, and on how to use official social media accounts to debunk election disinformation, he said.

In Houston, Chief Art Acevedo said that this year is the first in his long career when members of the public have asked about election safety.

"You have a sitting president already calling into question the election itself and whether or not it's a fixed election," he said. "So you're worried about if he loses, people actually believing that the election is fixed. And so when you put all that together and all the conflict in the country, we are worried. I think that most police chiefs are worried."