After a woman in Rockland County, N.Y., admitted to throwing her daughter a party while showing coronavirus symptoms, contact tracers sprung into action.

They phoned dozens of guests, hoping to get the partygoers tested and isolated and stop an emerging virus cluster in its tracks. But many of the attendees hung up, handed the calls to their parents or flat-out lied, saying they never made it to the event on June 17. Others never picked up at all.

So this week, county health officials tried a much more drastic approach. They issued subpoenas to eight of the partygoers, ordering them to speak up to the disease detectives or face a fine of up to $2,000 a day — and it worked.

“It’s amazing how smart some people got,” Ed Day, the county executive, told CNN on Thursday. “Everybody is complying and helping us, which is all that we’re trying to have happen. … We’re not looking to be punitive here.”

After some people across the country rose up against lockdown measures, ignored social distancing requirements and declared war on face masks, Rockland County’s unapologetic legal strategy shows just how difficult it may be to get Americans to comply with yet another government effort to fight the pandemic that has surged in recent weeks.

As The Washington Post has reported, many officials say the most effective way to curb the spread of the virus — short of another economic shutdown — is to conduct extensive contact tracing. Informing people who may have been exposed, getting them tested and quarantining those who are sick, they maintain, can curb emerging outbreaks without putting even more Americans out of work.

But this kind of detective work comes with a heavy logistical burden. State and local governments have to hire and train tens of thousands of tracers, act fast to keep up with the highly contagious virus, overcome government mistrust and privacy concerns and find money in their already cash-strapped budgets to fund it all.

It may become even harder as Americans increasingly get fed up with quarantining or act in plain defiance of public health guidelines. In Tuscaloosa, Ala., for example, officials said this week that college students have been organizing “covid parties,” where the attendees compete to see who can catch the virus first from a sick partygoer.

After officials found out about the party in the hamlet of West Nyack, involving between 50 and 100 people, nine guests tested positive for the virus. More large gatherings followed in a nearby town, and local officials have not publicly identified anyone involved.

Patricia Schnabel Ruppert, Rockland County’s health commissioner, said contact tracers could not get most of the partygoers, many of them young adults in their 20s, to answer even the most basic questions on the phone.

“My staff has been told that a person does not wish to, or have to, speak to my disease investigators,” Ruppert said at a news conference Wednesday. “They hang up. They deny being at the party even though we have their names from another party attendee.”

As Day, the county executive, threatened to issue the subpoenas, he added that he would not allow “ignorance, stupidity or obstinance” to get in the way of the county’s coronavirus response.

The pandemic struck the region, about 30 miles north of hard-hit New York City, badly and early on. More than 13,600 people in Rockland County tested positive for the virus, according to county data, and nearly 670 have died.

Only a handful of residents remain hospitalized as of Thursday, and the number of new infections reported each day have dropped to the single digits, the data shows. But as that figure started to increase this week, worried authorities offered a stern warning.

“If you get in the way of a health department investigation, we will take every step necessary to ensure we respond appropriately,” Day said, “and we’re talking a serious response."

Rockland County also issued subpoenas to contain a measles outbreak two years ago, when some residents resisted vaccinations, got sick and refused to quarantine.

Contact tracing, which can also be used to identify when likely patients may have been exposed, has also been highly successful outside the United States. In Germany and South Korea, the tactic has been used to isolate the sick and allow others to go back to their schools and workplaces.

An NPR analysis last month found that while the number of contact tracers tripled over a period of six weeks, the United States is still far from the estimated 100,000-plus workers needed to fight the virus nationwide. According to estimates from one virus model, only 12 states — including New York — and the District currently employ teams large enough to contain any flare-ups of the virus.

Last week, New York Gov. Andrew M. Cuomo (D) said his state’s robust contact-tracing system was able to identify emerging clusters at a graduation in Westchester County and at an aluminum factory and apple packaging facility further upstate.

With its 9,600 contact tracers, New York state appears to be in position to trace any new infections within 48 hours. Ahead of the Fourth of July holiday weekend, Day hopes they won’t be needed at all.

“If you are in a situation [where] you could get people sick or kill them,” he said, “you would think you would cooperate.”