As outgoing Homeland Security Secretary Kevin McAleenan sticks around amid a still-unsettled search for a successor, the man border hawks hope will take a harder line on immigration in that role is facing considerable political and legal barriers -- while some opponents push a more moderate candidate of their own.

Ken Cuccinelli, the current acting director of U.S. Citizenship and Immigration Services (USCIS) and a vocal immigration hardliner, has long been seen as one of the top candidates to replace McAleenan. In that office, he has introduced the “public charge” rule that clarified and toughened guidance on whether immigrants likely to be reliant on welfare should be given green cards -- a move that horrified Democrats and immigration activists.

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But those who want a more hardline immigration focus are encouraged by the prospect of Cuccinelli taking the job.

“Of the people who are being considered for the job, Cuccinelli would probably be the best one,” Mark Krikorian, executive director of the Center for Immigration Studies, told Fox News. “Cuccinelli is a quick study, he has become the face of the administration's immigration policy even beyond the responsibilities of USCIS and so far so good -- he seems to be doing a pretty good job.”

A former DHS official with close ties to the administration told Fox News earlier this month that Cuccinelli was at the top of President Trump’s list, while an administration official said that Cuccinelli was in “good standing.”

“Ken has been very effective on the regulatory side and he has proven to be a team player who will do every media hit no matter how small or how hostile,” the official said. “Ken is someone who hands-down supports and defends the work of the president and the administration.”

But another possible candidate is Acting Customs and Border Protection (CBP) Commissioner Mark Morgan, who has been an often-fiery defender of the work agents do on the ground in tackling illegal immigration. He too would be a pick welcomed by many immigration hawks like Krikorian.

And both their candidacies have been complicated in recent weeks. First, a legal hurdle in the form of the Vacancies Act -- which limits who can succeed an acting DHS chief -- has threatened to torpedo both Cuccinelli or Morgan. It limits candidates to those who have Senate approval, have worked under the previous secretary or are the next in line of succession.

As the White House decides what to do, a senior administration official told Fox News that Acting Secretary McAleenan, whose last day was supposed to be Thursday, will remain at DHS until a new pick is announced.

The New York Times reports that the White House has been exploring a possible loophole under which Cuccinelli or Morgan would be made the assistant secretary of the Countering Weapons of Mass Destruction Office and then bumped up to DHS a short time later. But it marks a risky strategy for the administration, since if that work-around is found to be invalid, it could mean challenges to any of the policies enacted under that secretary.

Coupled with that is political opposition not only from Democrats, but from some Republicans in the Senate, who are unhappy at the prospect of a Cuccinelli pick due to his past leadership of the Senate Conservatives Fund -- a group that seeks to primary sitting senators with more conservative challengers.

Majority Leader Mitch McConnell has in the past said he had expressed a “lack of enthusiasm” for Cuccinelli as a potential future DHS pick. Others have been starker in their warnings.

“The White House would be well advised to consult with the Senate and senators before they take any decisive action that might be embarrassing to Mr. Cuccinelli or to the White House itself,” Sen. John Cornyn, R-Texas, told Politico this week.

But other Republican senators have been glowing in their praise of Cuccinelli.

“Cuccinelli is already doing a fantastic job implementing President Trump’s priorities at DHS,” Sen. Mike Lee, R-Utah, told Fox News. “If he were nominated to be secretary he would have my vote and I am confident he would be confirmed.”

“Ken is a patriot who is well equipped to address our broken immigration system and the security and humanitarian crisis on the border. He would be an exceptional Secretary of Homeland Security,” said Sen. Ted Cruz, R-Texas.

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But as Cuccinelli faces that steep climb, increasingly the name of Chad Wolf, a senior DHS official and former chief-of-staff to former DHS Secretary Kirstjen Nielsen, has circulated as a possible McAleenan replacement. Wolf’s consideration was first reported by journalist Ryan Girdusky.

For those who oppose Cuccinelli, Wolf is a strong pick with a background of policy implementation, which they are contrasting against Cuccinelli’s relative lack of experience in immigration policy. A senior administration official told Fox News that Cuccinelli's stint in immigration is brief and leaves a vast mission for which, they say, he has no experience to back up.

Another senior official recommended Wolf in glowing terms.

"Anyone who knows him understands the tremendous asset he is to the DHS mission and the president's agenda. He's widely recognized as a trusted, committed and aggressive leader, credited with helping implement the policies developed to address the border crisis,” the official said. “His expertise is wrapped around the entire department and its many issue areas, from counterterrorism to election security. Hands down the most qualified."

But some of those same immigration hawks who support Cuccinelli are nervous over the prospect of a Wolf pick, particularly his past work as a lobbyist for a company that represents firms wanting to keep the H1-B visa program.

“Going with a career official or someone who once lobbied to replace American workers with cheap foreign labor sends the wrong signal right before an election year,” RJ Hauman, government relations director at the Federation for American Immigration Reform, told Politico last week. “President Trump can choose to be on the side of his base and American workers, or throw in his lot with the swamp.”

“There’s no question that immigration hawks would be upset with Wolf’s selection. In fact, the very fact he’s being considered for it is making people uneasy,” Krikorian told Fox News.

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Krikorian suggested that Wolf could be named as a temporary, short-term replacement for the acting secretary, with Cuccinelli then being tapped for Senate confirmation -- requiring the White House to sit down with McConnell and work out the differences.

“[McConnell] holds a grudge, but he’s also a grown-up,” he said. “Yes, it's possible they can overcome it, but without putting that work into it, and ironing out the legislative wrinkles ahead of time, then it’s entirely possible that McConnell won’t ever bring it up [for a vote] ever and you end up with Chad Wolf there next November.”

Late Thursday, The Wall Street Journal reported that the White House was considering a form of that plan, leaning toward tapping Wolf as acting secretary, but then moving instead toward Morgan as the eventual nominee for the permanent position -- a pick who would satisfy hawks without upsetting some Senate Republicans.

Cuccinelli on Friday was asked on "Fox & Friends" if he believed he was still in the running for the DHS job.

"I don't have a belief on that front," he said. "I just keep doing mine in the face of some people who would rather we weren't as successful as we've been all through the summer."

Fox News’ Brooke Singman and Leland Vittert contributed to this report.