The Paredes family plays a game of arm-wrestling at home in Northern Virginia. Family members could qualify for deportation relief under the proposed Deferred Action for Parents of Americans. (Nikki Kahn/The Washington Post)

President Obama’s embattled plan to provide temporary deportation relief and work permits to illegal immigrants with U.S.-born children — a proposal the Supreme Court is due to review this year — could benefit more than 10 million people in families with eligible members, increasing their household income by 10 percent, two research institutes said in a report released Thursday .

Obama announced the executive action in late 2014, but it was challenged in court by 26 states, which argued that he had overstepped his authority and that the program would impose an unfair financial burden on them. The program was blocked by federal courts; only a favorable high court ruling this summer would allow Obama to implement it before he leaves office.

[Border crossings down, but deportation raids to continue, ICE says]

According to the report by the Migration Policy Institute and the Urban Institute, both based in the District, the impact of Obama’s Deferred Action for Parents of Americans and Lawful Permanent Residents (DAPA) would resonate far beyond the estimated 3.6 million illegal immigrants, mostly from Mexico and Central America, whose children are U.S. citizens or legal residents.

The report found that the average household with at least one DAPA recipient could increase its income by about $3,000 if the recipient obtained a work permit and earned the same pay as a legal resident who had similar skills, educational ability and other traits. Currently, the report said, 36 percent of families eligible for DAPA live below the poverty line; the average income for such families is $31,000.

About 1 million people are eligible for DAPA in California, followed by Texas and New York. Virginia ranks 12th, with 61,000, and Maryland ranks 13th, with 56,000.

Obama announced a second action in 2014 offering similar benefits to an expanded group of young illegal immigrants, which also was blocked by the courts. Both initiatives were among a series of Obama administration efforts to help some of the country’s estimated 11 million illegal immigrants gain legal relief after Congress failed to enact comprehensive immigration reform.

[Obama struggling with immigration rules, cruelty of deportations]

Many critics, including a majority of Republicans in Congress and the top Republican candidates for president, have opposed Obama’s executive actions as conferring “amnesty” on illegal immigrants and have said they would cancel such programs.

Immigrant advocacy groups across the country have said that if the Supreme Court rules favorably on DAPA this summer, they will be ready to help millions of people apply as quickly as possible. Many have held workshops instructing older illegal immigrants to gather their income, rent, identity and other documents so they can apply right away.

The program would offer those with clean police records, proof of long-term residency and other documentation a three-year initial reprieve from deportation and a work permit with a Social Security card.

[The anchor pulls in many directions]

The report found that although they are poorer than other families with underage children, DAPA-eligible families are “well-settled with strong U.S. roots.” It found that 69 percent of illegal immigrants eligible for DAPA, mostly born in Mexico, have lived in the United States for at least a decade, and that one-quarter have lived here at least 20 years. It also said that about 85 percent of underage children living with DAPA-eligible parents are U.S. citizens who were born here.

The report found that 95 percent of men eligible for DAPA are in the U.S. labor force, so obtaining the new benefits would have “little impact” on labor-force participation. Only 52 percent of eligible women are working, but the report said that percentage was unlikely to grow significantly.

Most illegal immigrants work in menial jobs such as agricultural fieldwork, restaurant kitchen work, hotel and office cleaning, landscaping, and semi-skilled construction.

[A pre-dawn knock, and then they were gone]

The report followed studies by the institutes that found in homes where children are U.S.-born but their parents remain in the country illegally, those children can be held back from succeeding because of family stress, fear of parents being deported, poverty and reluctance to seek services and benefits.

“Fear of deportation is ever-present in these families,” the report said, noting that the deportation of a DAPA-eligible father would reduce family income by an average of $24,000 a year, changing its economic status from “near-poor” to “deep poverty.”

If the Supreme Court permits DAPA to go ahead, the report said, “the program has the potential to improve the incomes and living standards for many unauthorized immigrant families.”