The Trump administration’s now-rescinded policy of separating children and parent migrants to deter illegal immigration was a political belly-flop, with Trump rescinding the policy after bipartisan backlash. But Trump may stand on sturdier political footing in the next stage of debate over how to deal with families accused of crossing the border illegally, according to a Washington Post-Schar School poll released last week.

The survey found Trump’s initial policy was widely unpopular, with about 7 in 10 Americans opposed to separating children from parents who are accused of entering the U.S. illegally through the southern border, including about 9 in 10 Democrats and three-quarters of independents. Just over 6 in 10 Republicans supported the now-reversed policy.

But a follow-up question asking what should happen to families accused of crossing illegally found most Americans supporting a relatively punitive approach. A 58 percent majority said they prefer that these families be held together in a detention facility until their immigration case is resolved, while 39 percent said they should be temporarily released until a deportation court hearing.

The finding suggests most Americans agree with the Justice Department’s request to a federal court to allow Immigration and Customs Enforcement to hold families with children in detention together until their cases are adjudicated. Doing so would require modifying a long-standing court settlement that requires children to be released from detention facilities within 20 days.

As The Post’s Maria Sacchetti and Tony Perry reported Monday, a federal judge in California sharply rebuked that request. The result is that reunited families will be released and allowed to stay in the United States pending further immigration proceedings — “the exact opposite of what President Trump and Attorney General Jeff Sessions had hoped to accomplish when they launched the 'zero tolerance' effort in May."

Despite the legal setback, the Post-Schar School poll shows broad support for the policy Trump administration lawyers pushed for, including among a wide range of political groups. Keeping immigrant families in detention rather than releasing them garners support from 74 percent of Republicans and 60 percent of independents. Democrats — 89 percent of whom disapprove of Trump’s handling of immigration — are almost evenly split on the question, with 49 percent saying families should be detained, while 50 percent say they should be temporarily released.

There is little gender gap on the question, with 59 percent of men and 57 percent of women preferring to detain immigrant families together until their case is resolved. That compares with child-parent separations, about which women were 25 percentage points more likely than men to say they “strongly opposed” (65 percent vs. 40 percent).

Comparing this issue with child-parent separations directly, 84 percent of those who support that now-rescinded policy also prefer to hold families in detention rather than temporarily release them. Those who oppose child-parent separations are split on detention, with 48 percent saying families should be detained together, while 49 percent say they should be released until an immigration hearing.

This doesn’t necessarily mean Trump would win a public political argument over detaining migrant families. One reason is that the survey’s questions described the child-parent practice as the “Trump administration policy” but asked the question on future status immigrants without mentioning Trump’s view. Trump’s majority disapproval rating overall and on immigration in particular could drag support for detaining families indefinitely during an extended debate.

In addition, because mass detainment of immigrant families has not yet occurred, public reactions could shift after the policy took effect. The Post-Schar School poll found 74 percent of Americans saying they were bothered by photos of children being separated from their parents and held in detention centers, with 48 percent bothered “a lot.” It’s possible that large-scale family detentions would spur similar public backlash and sympathy.

Still, the survey’s finding of support for family detentions is a signal that the public continues to widely support ramping up efforts to deter illegal immigration and is open to some punitive measures aimed at achieving this. The Post-Schar School poll found a 65 percent majority of adults supported increasing funding for border security programs, including majorities of Democrats (52 percent), independents (66 percent) and Republicans (90 percent).

The ways Americans assign blame for child-parent separations also suggests the public’s sympathy toward undocumented migrants is limited. Some 37 percent said the Trump administration was more to blame for immigrant children being separated from their parents, but almost as many (35 percent) blamed migrants trying to enter the United States illegally. Another 25 percent said both deserved equal blame.

The Post-Schar School poll was conducted June 27-July 2, 2018, among a sample of 1,473 adults interviewed through the AmeriSpeak Panel, the probability-based panel of NORC at the University of Chicago. Interviews were conducted online and by landline and cellular phones. The margin of error for overall results is plus or minus five percentage points.

Emily Guskin contributed to this report.