WASHINGTON >> President Donald Trump says there’s only one person in charge of his immigration policy: Him.

Asked by reporters today whether he had considered tapping his influential aide, Stephen Miller, to lead the Department of Homeland Security given Miller’s focus on the issue, Trump was ready with praise — but not a promotion.

“Stephen is an excellent guy. He’s wonderful person… He’s a brilliant man,” Trump said as he departed for Texas. But “frankly, there’s only one person that’s running it,” Trump said. “You know who that is? It’s me.”

Trump on Sunday announced that Kevin McAleenan, the commissioner of United States Customs and Border Protection, would be taking over as acting secretary in the wake of Kirstjen Nielsen’s sudden departure.

Asked whether Trump was considering nominating McAleenan as his permanent secretary, Trump said “could happen.”

“We have others, but right now he’s the man,” said Trump.

The comments came a day after Trump said he was not looking to revive the much-criticized practice of separating migrant children from their families at the southern border, as he has privately threatened, amid bipartisan pushback to his shake-up at Homeland Security. At the same time, he suggested the policy had worked to deter migrants from coming into the U.S., although he offered no evidence to support his position.

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 on Tuesday 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 Trump’s tenure was just one aspect of the upheaval at the Department of Homeland Security this week that culminated with Nielsen’s resignation. Acting Deputy Secretary Claire Grady, a 28-year civil servant, technically next in line for secretary, was forced to resign Tuesday to make room for Trump’s pick to replace Nielsen, according to two people familiar with the decision.

With talk that more top officials were likely to be ousted, 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.

House Oversight Committee Chairman Elijah Cummings, D-Md., said his committee would look at the staff shake-up at Homeland Security, although he said he had not decided on calling 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.

At hearings across Capitol Hill, lawmakers also grilled administration officials on whether the family separation practice would resurface despite last year’s outrage and evidence that separations were likely to cause lasting psychological effects on the children.

People familiar with immigration discussions within the administration said family separation was one of several ideas Trump had revived in recent weeks as he and his aides try 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 to The Associated Press on condition of anonymity.

A senior administration official who briefed reporters on condition of anonymity Tuesday said the president had made a series of leadership changes at DHS because of frustrations that department officials weren’t fast enough at implementing changes, such as a new regulation that would challenge a longstanding agreement limiting how long children can be detained.

The White House also was weighing a tougher standard to evaluate initial asylum claims, proposing a “binary choice” that would force migrant families to choose between remaining with their children in detention until their immigration cases were decided or sending their children to government shelters while the parents remained in detention.

The administration also is considering clamping down on remittance payments that Mexican nationals send to their families, the official said.

Amid the pushback, Trump told reporters he was not “cleaning house” at the agency despite the numerous staff changes.

But as Trump was speaking, the senior administration official was making a case to reporters about why the president felt changes were necessary. He described the agency as a large and unwieldly civilian bureaucracy in need of leadership that can deal with career officials resistant to the president’s agenda, including many responsible for implementing some of the very policies Trump seeks to roll back.

Top Republicans in Congress also expressed concern over vacancies at Homeland Security and cautioned Trump to heed off more churn after Nielsen’s resignation.

Sen. Chuck Grassley, R-Iowa, made both a public and private plea to the White House not to dismiss career homeland security officials, including the director of United States Citizenship and Immigration Services, Lee Francis Cissna, whose future remained uncertain Tuesday.

He said he had spoken to acting chief of staff Mick Mulvaney but “never heard anything final” about Cissna.