In Hempstead, a Long Island town where the typical property tax bill tops $10,000, residents have lined up all week to prepay those taxes for next year. They have been trying to save thousands of dollars before the new federal tax bill, which goes into effect on New Year's Day, sharply limits deductions for state and local taxes.

But late on Wednesday, the Internal Revenue Service issued new guidance that those people may not be able to save the money after all, because a loophole that they were hoping to exploit might be narrower than thought. So when Donald X. Clavin Jr., Hempstead's receiver of taxes, showed up to work Thursday morning, the lines were still there — but residents had fresh questions. Mr. Clavin had few answers.

"Everybody on line, they're going, 'Don, are we going to be able to do this?' " Mr. Clavin said. "And I can't give them a yes or a no."

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The new tax bill, and its $10,000 cap on all local and state tax deductions, has generated a variety of strong emotions — including anxiety and frustration — in places like Hempstead.

By Thursday, however, that stew of emotions had been replaced by utter confusion, as well as rage, including among people who had shelled out money only to discover that they might not get any benefit.

This week's tax-prepayment roller coaster could be just the beginning. Republicans pushed through their tax overhaul at blistering speed, giving lawyers and accountants only about a week to study the bill before it goes into effect.

But already, those people studying the law have uncovered internal conflicts and unintended consequences, as well as broad areas of uncertainty the I.R.S., the Treasury Department and, ultimately, the court system will be left to resolve.

"It's fun if you're a tax lawyer," said David Herzig, a professor of tax law at Valparaiso University. "I'm not sure it's fun if you're a person going through it."

The confusion this week stems from the provision in the new tax bill that caps the previously unlimited deduction for state and local taxes, and the I.R.S. guidance about the ability of people to prepay property taxes this year.

In Hempstead, and in other high-tax, high cost-of-living communities across the country, tax bills routinely run far above the new $10,000 threshold once state income and local property taxes are taken into account. In Nassau County, which includes Hempstead, the average state and local tax deduction in the county, including property taxes, topped $20,000 in 2015, among the highest in the country, according to data from the I.R.S.

The new cap does not take effect until January, however. The tax bill explicitly prevented people from prepaying state income taxes, but it did not address prepayment of property taxes. That gave homeowners a brief window to pay their 2018 property taxes in 2017, and to take the full deduction when they file their federal returns this spring.

Officials in Chicago, Washington, Fairfax, Va., and other communities reported huge surges of residents prepaying taxes, often showing up in person, checks in hand. Democratic politicians, who have opposed the bill, egged them on, arguing that the bill targeted states that tend to vote for Democrats.

Even before President Trump signed the bill into law last week, local officials in Washington announced they would accept prepayments in what the city's mayor, Muriel Bowser, called a bid to "protect Washingtonians from the negative impacts of this devastating legislation." Gov. Andrew Cuomo of New York last week signed an executive order opening the door for prepayment, a move he freely described as a bid to circumvent the new law. Local officials in Maryland, Virginia and other states made similar moves.

Even Chris Christie, the Republican governor of New Jersey and an early supporter of Mr. Trump's, on Wednesday signed an executive order instructing local officials to accept prepayments.

The I.R.S. memo, however, threw many of those efforts into question. The memo said that property taxes paid this year would be subject to the old 2017 rules — but only if the taxes are actually assessed in 2017. That means that payments based on estimated assessments, or for years further in the future, probably would not qualify for the deduction.

Final answers might not be available anytime soon. The I.R.S. guidance left plenty of room for interpretation and was, in any case, nonbinding.

But the memo had an immediate impact. In Prince George's County, Md., the County Council had been planning to hold an emergency session on Thursday to discuss letting residents prepay their taxes, a step already taken by neighboring Montgomery County. But within hours of the memo's release, the council canceled the meeting.

Dannielle M. Glaros, chairwoman of the Prince George's County Council, said the I.R.S. guidance left her little choice. T he decision to cancel the meeting resolved the immediate uncertainty, but it did little to ease residents' larger confusion about the effects of the bill.

"It's this sense of the unknown," Ms. Glaros said. "That is what's creating a lot of this anxiety that we're seeing."

Anxiety — and also anger. Steve Halliwell, who lives with his wife, Anne, in Irvington, a village in Westchester County, N.Y., began asking town officials several weeks ago about paying next year's property taxes this year. Mr. Cuomo's executive order last week was meant to make that possible.

But the order came too late for the county's residents: Officials there said this week that they would not be able to issue tax assessments by the end of the year.

"There are a lot of angry people here because they feel powerless and they are not used to feeling powerless," Mr. Halliwell said. "This shows the venal side of politics."

Other communities happily accepted the money — but offered no guarantees that prepaying would work out for taxpayers.

In Clarkstown, in Rockland County, N.Y., residents began lining up at the tax office before 9 a.m. on Thursday. The line snaked down the hall as hundreds of residents waited to get their property tax bill and then pay it. Outside, the parking lot was so crowded that police officers directed traffic.

"We brought in extra staff and extended the hours," said George Hoehmann, the town's supervisor. "We have gotten thousands of calls. Normally, it would be quiet this time of year, but there is a lot of anxiety because people don't know what the impact of the tax bill will be."

In the last two days, more than 3,500 people came in to prepay their 2018 property taxes, 2,000 of them on Thursday. "I've seen nothing like this ever," said Mr. Hoehmann, who has been town supervisor for three years and was a councilman for seven years before.

Mr. Hoehmann said he believed the town's residents would get the tax break under the I.R.S. ruling. The town had already assessed the 2018 property tax bill, allowing residents to prepay their town, county and special district taxes in 2017, he said.

But he also made no promises.

"Ultimately that's between the individual taxpayer and the I.R.S.," he said. "We advised people to speak to their accountant. What we wanted to do was give them the opportunity."

Some taxpayers took the uncertainty in stride. Chacko Kurian, who lives in Rockland County, was in line Thursday morning to pay some of the $30,000 in property taxes he owed on his house, which he described as a "mansion" with a fish pond and a waterfall.

Mr. Kurian, a 70-year-old retired engineer for the Metropolitan Transportation Authority, said he did not know whether prepaying his taxes would work out. But he figured it was worth the risk.

"My accountant said prepay and see what happens," Mr. Kurian said. "You can't fight the system. It is what it is."