Now, some immigration hawks are worried Trump will never nominate a permanent secretary, leaving Wolf as acting secretary. Or, worse yet, they fear Trump will eventually nominate Wolf to run the agency full time.

“Three things must happen to quell the base's concerns,” said RJ Hauman, government relations director at the Federation for American Immigration Reform, which favors immigration restrictions.

“First, Wolf must recuse himself from all work on guest worker related issues" because of his past lobbying work, Hauman said. "Second, he needs to publicly commit to President Trump's immigration agenda. Third, and perhaps most importantly, there must be an official nomination in the next week to show that Wolf’s tenure as acting secretary is just temporary.”

A senior DHS official defended Wolf when asked about immigration hawks’ concerns.

“Wolf has worked to advance the president’s bold, security-focused agenda from Day One of the administration," the official said. "He's an experienced and widely respected leader with a deep understanding of the department’s dynamic mission, its challenges and priorities — from securing our borders, to upholding our laws and protecting American workers. An invaluable asset to the cause and all we do."

And a senior administration official argued that the president's immigration policies had actually been effective, citing, among other things, the reduction in illegal border crossings and the decline of overcrowding at DHS immigration facilities.

"It’s sad, but not surprising, that open borders advocates would oppose this progress, but the reality is they will only be satisfied by a system [more] akin to full blown lawlessness than anything else," the official said.

Trump announced in October that Kevin McAleenan would step down as acting DHS secretary after serving just six months. Although McAleenan oversaw a reduction in the number of migrants caught at the southwest border, Trump allies complained he wasn’t fully implementing the president’s policies.

Similar concerns have caused Trump to burn through four DHS secretaries in less than three years. Six other top department officials have resigned or been pushed out since April for largely the same reasons. Many of the department‘s senior leadership positions remain vacant or filled by acting officials.

“There's just a lot of resignation that we can't spend anymore time worrying about it,” said a former DHS official who served in a Republican administration. “Everybody's just worn out because it's been 2½ years of white-hot focus.”