In his survey, Peter DeGroot, head of municipal research and strategy at J.P. Morgan, found a handful of states, including Idaho, South Dakota and New Mexico, that managed to take in even more money last year than in 2019. The survey also identified several states where tax revenues have not yet bounced back because they depend heavily on tourism, oil and gas, or coal extraction — among them Hawaii, Nevada, Florida, Texas and West Virginia.

Ms. Sheiner’s analysis showed that Idaho had the biggest revenue recovery of any state. She conducted her research with Byron Lutz, an economist with the Federal Reserve.

The head of Idaho’s Division of Financial Management, Alex J. Adams, said in an interview that the rebound had taken officials by surprise, and that they thought one reason was an influx of new residents from California, seeking to escape that state’s high cost of living — a trend that started before the pandemic but accelerated last year. Mr. Adams also said Idaho didn’t pause construction when the lockdowns happened, which helped economic activity.

Idaho’s Republican governor, Brad Little, said in his State of the State address in January that 2020 revenue collections were strong enough to send $295 million back to the taxpayers, and still have enough to invest in better highways, bridges and broadband access. He also wrote to Idaho’s congressional delegation last year, urging it to oppose the use of no-strings federal dollars to bail out mismanaged states.

With some states now “enjoying windfalls” and others still struggling, Mr. White said a smaller amount of money, more carefully targeted to the states that needed it most, would be the most efficient approach for Congress. But getting assistance to those governments that truly need it, without sending unnecessary aid to those that do not, will require some “exceptional creativity,” he said.

To some extent, the states’ surprising recoveries reflect the timing of events last year. The pandemic started just as many state lawmakers were reviewing initial budget proposals for the coming fiscal year. The proposals, drawn up weeks before the shock, forecast a year of strong tax collections.

Then, in a matter of weeks, millions of people lost their jobs. State officials think of unemployment as a powerful driver of their fiscal affairs; research from past recessions suggests that a single percentage-point increase in the unemployment rate can produce $45 billion worth of state budget woe.

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