Thousands of federal programs are affected by the shutdown, but few intersect with the public as much as the tax system and the Department of Agriculture’s Supplemental Nutrition Assistance Program, the current version of food stamps.

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The partial shutdown has cut off new funding to the Treasury Department and the USDA, leaving them largely unstaffed and crippling both departments’ ability to fulfill core functions.

The potential cuts to food stamps and suspension of tax refunds illustrate the compounding consequences of leaving large parts of the federal govern­ment unfunded indefinitely — a ­scenario that became more likely Friday when President Trump said he would leave the government shut down for months or even years unless Democrats gave him money to build a wall along the U.S.-Mexico border.

The SNAP program is rare among federal initiatives because it requires annual funding from Congress, even though its existence is automatically renewed.

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Congress has not allocated funding for SNAP beyond January, and the program’s emergency reserves would not cover even two-thirds of February’s payments, according to past disbursements. Last September, the most recent month for which data is available, SNAP disbursed $4.7 billion in benefits to recipients across every U.S. state.

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Lawmakers last year appropriated $3 billion into a “contingency” fund for SNAP. USDA officials would not comment on the status of the $3 billion, but if all of that money is still available, it would cover just 64 percent of February’s obligations.

Agency officials have not said how they would address the shortfall, including whether they would prioritize who receives food aid or cut benefits for everyone across the board.

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If the shutdown continues through March, there would be no remaining money for benefits.

“We are currently looking at options for SNAP,” said Tim Murtaugh, a spokesman for the Agriculture Department. “The best course of action would be for Congress to pass a legitimate appropriations bill to the president to end the lapse in funding.”

During the shutdown, the USDA office that administers SNAP has sent home 95 percent of its employees without pay, according to a flowchart on the department’s website.

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“People in this country will go hungry,” said Rep. Rosa L. DeLauro (D-Conn.). “It’s simple. They go hungry. . . . These are working people. We’re not talking about people who are dogging it.”

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The disruption would hurt not only the families that receive the assistance but also grocers and other retailers where the money is spent.

Treasury Department officials, meanwhile, are trying to determine what to do with the flood of requests for tax refunds that will come in next month.

The Internal Revenue Service has sent home close to 90 percent of its staff without pay ahead of an extremely busy time for the tax agency.

From late January through March 2 of 2018, the IRS paid out $147.6 billion in tax refunds to 48.5 million households. That money could be frozen within the IRS if the refunds are stalled.

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Early last year, as part of its contingency planning for possible government shutdowns, the IRS said it would not issue any tax refunds during a shutdown. Treasury and IRS officials have not said they will completely suspend all tax refunds next month, but a senior administration official said such disbursements would be severely affected and likely slowed if they are paid.

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House Ways and Means Committee Chairman Richard E. Neal (D-Mass.) sent a letter to Treasury Secretary Steven Mnuchin on Friday asking him to detail the impact of job cuts at the IRS and how the tax filing season will be handled during the shutdown.

“Please confirm whether the IRS will issue federal tax refunds at any time during government shutdown,” the letter said. “If so, please provide the anticipated date when the IRS will be issuing refunds.”

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This could have an immediate impact on the economy, as well as on the finances of millions of Americans who frequently spend their tax refunds soon after receiving them.

“The IRS will finalize and release its filing season lapse plan in the coming days,” said a Treasury Department official, who, like others, spoke on the condition of anonymity because he wasn’t authorized to discuss the internal planning.

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Under normal schedules, tax returns for income earned in 2018 would be due April 15. People who anticipate receiving a tax refund — meaning they overpaid their taxes last year — tend to file their taxes as early as possible to recoup the funds quickly.

“It would be a huge political and economic hit for people who are expecting their $2,500 or $3,000 refund to not be able to get that money,” said Mark Mazur, a former top IRS official who served at Treasury during the Obama administration.

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Trump has said he is willing to keep agencies shut down as long as necessary to force Democrats to appropriate several billion dollars for the construction of walls along the Mexico border. But some Republicans have said they are uncomfortable with this approach, and several this week sided with Democrats in their effort to reopen agencies immediately.

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The scale of the consequences also reflects a deep disconnect between Trump, who has largely cheered on a prolonged shutdown, and the officials running federal agencies, who are trying to minimize the fallout.

“If we have to stay out for a very long period of time, we’re going to do that,” Trump said Friday.

White House officials have not fully briefed lawmakers on the expanding consequences of the government shutdown, leading to confusion about what happens as each week goes by.

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Neal said that the IRS is considering bringing staffers back to work in the coming weeks to help deal with tax filings but that it’s unclear how the agency will proceed. These employees would have to work without pay unless Congress passed an emergency funding bill. He said delays in tax refunds would lead to “more anger, for something that can be solved.”

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Rep. Mark Meadows (R-N.C.), a top House conservative who had cheered Trump’s approach in the political confrontation, said he was unaware that there would be any impact on SNAP benefits.

He said he was convinced this money was automatically appropriated by Congress: “Food stamps go on regardless,” he said.

This is not the case, however, according to several senior administration officials.

Meadows said he was “not downplaying the potential consequences of a shutdown,” but said the whole situation could be easily resolved if Democrats would appropriate several billion dollars for the border wall.

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The government shutdown began Dec. 22 after Trump blocked a bipartisan deal to fund numerous federal agencies through Feb. 8 because he wants more than $5 billion to construct 200 miles of wall along the border.

During his campaign and earlier in his presidency, Trump said the wall would be paid for by Mexico. That has not happened.

The shutdown began with an acute impact, cutting off funding to pay 800,000 federal employees, closing national parks and museums, and limiting federal services. The workers are expected to begin feeling the consequences of the shutdown more sharply next week: They will miss their first paychecks on Jan. 11 if a resolution isn’t reached.

“A month into this, we’re going to see people start to get evicted and their cars start to be repossessed,” said David Borer, general counsel for the American Federation of Government Employees, which represents 750,000 federal employees.

And a much broader part of the federal bureaucracy is expected to begin grinding to a halt in February, absent a resolution.

Nonprofit groups have been able to patch together money to keep certain parts of the government open for several weeks, but it’s unclear how much longer they can hold on. And none has sought to replicate the level of funding that would be lost if SNAP runs out of money or tax refunds are stalled.

“That’s scary, really scary,” said Lyman Hafen, executive director at Utah’s Zion National Park Forever Project, a nonprofit partner of one of the country’s most scenic parks. “It’s not a good situation without that support. We’re just taking it a day at a time, a week at a time.”

The cumulative impact of these changes could have a major impact on the economy.

Joseph Brusuelas, chief economist at RMS U.S., an accounting and consulting firm, said a prolonged shutdown would shave an entire percentage point off the U.S.’s economic growth, in part because of an “uncertainty tax” that would freeze spending by households and businesses.