Millions of immigrants benefiting from President Obama’s executive actions could get a windfall from the Internal Revenue Service, a reversal of fortune after years of paying taxes to help fund government programs they were banned from using.

Armed with new Social Security numbers, many immigrants who were living in the United States illegally will be able to claim up to four years’ worth of tax credits designed to benefit the working poor. For big families, that’s a maximum of nearly $24,000, as long as they can document their earnings during those years.

Advocates argue that many immigrants pay taxes, so they should be able to claim the same tax credits as anyone else. During the past decade, illegal immigrants have paid an estimated $100 billion in Social Security payroll taxes, even though few will be able to collect benefits, said Stephen Goss, Social Security’s chief actuary.

Obama has issued executive orders shielding about 4 million immigrants from deportation. Some were brought here as children; others are parents of children who are American citizens or legal residents.

Republicans in Congress oppose Obama’s actions and are trying to use a funding bill for the Department of Homeland Security to overturn them. Democrats are resisting, resulting in a stalemate that threatens to shut down the department.

Funding for the department, which oversees immigration enforcement, will run out on Feb. 27.

The dispute over tax credits illustrates the complicated relationship that many immigrants have with the tax system. Social Security estimates that illegal immigrants work at about the same rate as the rest of the population, even though federal law bars them from employment.

For those who work and pay federal income taxes, the IRS provides them with an Individual Taxpayer Identification Number. Since 1996, the IRS has issued 21 million such numbers. About a quarter of them are in use, the agency says.

The IRS accepts these tax returns without reporting the taxpayers to immigration authorities, IRS Commissioner John Koskinen said. That encourages the workers to pay taxes.

“We don’t enforce the Social Security laws. We don’t enforce the immigration laws,” Koskinen said of his agency. “In fact, the reason illegal immigrants file taxes with us is they know we aren’t sharing that data with anybody. We treat it as taxpayer-protected information.”

Even if immigrants pay taxes, they are ineligible for most federal programs. They cannot legally get food stamps, unemployment benefits, Pell grants or federal student loans. They cannot get Medicaid, except for emergency medical services, and are ineligible for subsidies under Obama’s health law. They can claim some federal tax breaks if they file tax returns, but until now, they were not eligible for Social Security, Medicare or the Earned Income Tax Credit, one of the government’s largest anti-poverty programs.

Obama’s executive actions will offer Social Security numbers to these immigrants, something that eventually could make them eligible for Social Security and Medicare.

More immediately, they could take advantage of the EITC. Last year, the credit provided low-income workers with about $70 billion.

The credit is popular among conservatives because it rewards work — the more you work, the bigger your credit, as long as your income does not exceed certain limits. It is popular among liberals because it provides cash payments to low-wage workers, even if they do not make enough money to pay federal income taxes.

Once the immigrants receive Social Security numbers, they can file tax returns claiming the EITC, as long as they meet the income requirements and can document their earnings.

There’s more.

They can file amended tax returns for up to three years after they were due, which means these immigrants can claim tax credits going back as far as 2011.

The maximum credit for families with three or more children is about $6,000, so some could get as much as $24,000 in credits.

Some members of Congress are outraged.

“The administration may have blown open the doors for fraud with amnesty bonuses of more than $24,000 to those who receive deferred action,” said Sen. Ben Sasse, R-Neb. “This program severely undermines the White House’s lip service to enforcing the law, and would increase the burden on law-abiding taxpayers.”

Advocates for immigrants say that if these workers are paying taxes, they should get the same benefits as other taxpayers.

“Let’s not forget that these workers receive the lowest wages for what they contribute to their communities and local economies,” said Ellen Sittenfeld Battistelli, policy analyst at the National Immigration Law Center. “What do we as a nation gain by further impoverishing them?”