WASHINGTON — Facing bipartisan pushback on his immigration shake-up, President Donald Trump said Tuesday he’s not looking to revive the much-criticized practice of separating migrant children from their families at the southern border. At the same time, he suggested the policy had worked to deter migrants from coming into the U.S.

Immigration experts say his policies and practices are contributing to the surge of migrants.

Last summer the administration separated more than 2,500 children from their families before international outrage forced Trump to halt the practice and a judge ordered them reunited.

“We’re not looking to do that,” Trump told reporters before meeting with Egypt’s president at the White House. But he also noted: “Once you don’t have it, that’s why you see many more people coming. They’re coming like it’s a picnic, because let’s go to Disneyland.”

The potential reinstatement of one of the most divisive practices of the Trump administration was just one aspect of the upheaval evident at the Department of Homeland Security this week following the resignation of Secretary Kirstjen Nielsen. With talk that more top officials were likely to be pushed out, Republicans expressed public and private concerns about the shake-up orchestrated by the White House and cautioned that leadership changes wouldn’t necessarily solve the problem.

As for the separation of children, Trump declared that he was “the one that stopped it” and said President Barack Obama, was the one who had divided family members. The administration is allowed to separate children under certain circumstances including the health and welfare of the child and a parent’s criminal history. This is why children were separated under the Obama administration.

At hearings across Capitol Hill, lawmakers grilled officials on whether the practice would resurface despite last year’s outrage and evidence that separations were likely to cause lasting psychological effects on the children. House Oversight Committee Chairman Elijah Cummings said his committee would take a look at the staff shake-up at Homeland Security, and said he was deciding whether to call in Nielsen.

Sen. John Kennedy, R-La., said there was a serious problem going on between the White House and Homeland Security.

“If everybody’s sitting around waiting for a shiny new wonder pony to ride in and solve it, we’re going to be waiting a long time,” he said.

People familiar with the immigration discussions within the administration said family separation was one of many suggestions that Trump and his aides were eyeing to tackle the problem of an ever-growing number of Central American families crossing into the U.S. The people were not authorized to speak publicly and spoke on condition of anonymity.

A senior administration official who briefed reporters on condition of anonymity said the White House would move forward with a new regulation that would challenge a long-standing agreement limiting how long children can be detained, hoping to spark a legal fight that would land in the Supreme Court.

The White House also was weighing a tougher standard to evaluate initial asylum claims, a “binary choice” that would have migrant families choose between remaining with their children in detention until their immigration cases are decided or sending their children to government shelters while the parents remain in detention. It also is considering clamping down on remittance payments that Mexican nationals send home.

Amid the turmoil, Trump told reporters he was not “cleaning house” at the agency despite a number of staff changes. He said his choice to be the department’s new acting director, Kevin McAleenan, would do a “fantastic job.”

But at the same time that Trump was speaking, the senior official was describing DHS to reporters as a large and unwieldy civilian bureaucracy that needs leadership that can deal with career officials resistant to the president’s agenda, including many who were responsible for implementing some of the very policies Trump seeks to roll back.

Top Republicans in Congress expressed concern over vacancies at Homeland Security and cautioned Trump about more churn after the resignation of Nielsen.

Sen. Chuck Grassley, R-Iowa, made both a public and private plea to the White House not to dismiss career Homeland Security officials. He said he spoke to acting chief of staff Mick Mulvaney but added that he would only know if Trump heard the message “if they don’t get fired.”

At a Senate Homeland Security Committee meeting on border issues, child welfare and border officials warned there wasn’t room or capability to start separating children on a large scale again.

Children who cross the border alone are cared for by the Department of Health and Human Services, and most of the children are teenagers. But last summer, HHS started receiving babies and toddlers, and there was not enough space to house them, said Jonathan White, the career civil servant tasked by Health and Human Services with helping to reunify children.