WASHINGTON — House Republicans moved to kick the migrant crisis created by President Trump back to the White House on Tuesday by scheduling a vote for a broad immigration bill that is unlikely to pass before Congress goes on break, and almost certainly would be a nonstarter in the Senate if it does.

After failing to pass a conservative immigration overhaul last week, deeply divided House Republicans faced similar low odds for success as they planned a second vote Wednesday on legislation that would fund a border wall and curb legal immigration programs, as well as provide legal status for so-called Dreamers and keep families together in detention.

Congress is set to recess on Thursday for an extended July 4 holiday, so the focus on the so-called compromise bill is likely to run out the clock before lawmakers can consider a much more limited proposal that would seek to fix only the family separations crisis.

The impasse will keep the emotionally charged controversy in the public eye as lawmakers return to their districts five months before the midterm elections amid growing concerns that the Trump administration has been unable to fully account for more than 2,000 migrant children who were detained separately from their parents since May.

The controversy widened Tuesday as 17 states sued the Trump administration for what they alleged was “cruel and unlawful” separation of migrant families.

The suit, filed in federal court in Seattle, objects to the policy of refusing entry to asylum seekers at the U.S.-Mexico border. It also says Trump’s executive order on June 20 to stop the family separations was “illusory.”

The lawsuit claims Trump’s order is riddled with caveats and fails to reunite parents and children who already were separated.

It accuses the administration of denying the parents and children due process under the law and of being arbitrary in applying its policy. It also accuses the administration of denying the immigrants, many of whom are fleeing gang violence in Central America, their right to seek asylum under U.S. and international law.

The states joined in the lawsuit are California, Delaware, Illinois, Iowa, Maryland, Massachusetts, Minnesota, New Jersey, New Mexico, New York, North Carolina, Oregon, Pennsylvania, Rhode Island, Vermont, Virginia and Washington. All have Democratic attorneys general.

Trump has blamed Democrats for the stalemate in Congress, but he has given wildly mixed signals about what he wants from Republicans there.

The president initially said he opposed the compromise bill, then told Republican lawmakers he was 1,000 percent for immigration legislation, and then said Republicans “should stop wasting their time” by trying to pass a bill before the November elections.