PALM BEACH, Fla.—President-elect Donald Trump, coming off a steady two-week flow of personnel announcements for his nascent administration, is confronting a series of more vexing decisions about how to shape the remainder of his cabinet.
Chief among them is whether to name as secretary of state Mitt Romney , who emerged as Mr. Trump’s early favorite for the post despite his criticism of the GOP nominee during the Republican presidential primaries. The campaign against the party’s 2012 presidential nominee escalated Sunday when Kellyanne Conway, a top Trump adviser, said on CNN that a “breathtaking” number of people would feel “betrayed” if Mr. Romney got the prominent cabinet post after he had opposed Mr. Trump so publicly.
A spokeswoman for Mr. Romney, who has met and spoken privately with Mr. Trump about the State Department job at least twice, didn’t respond to a request for comment.
The internal tug of war over who will be named to the nation’s top diplomatic job has slowed what had been a relatively brisk pace of appointments since Vice President-elect Mike Pence took over the transition effort a week after Election Day. It also is obscuring the many key positions that remain unfilled.
Mr. Trump has interviewed for—but not filled—the defense secretary post, saying he is seriously considering retired Gen. James Mattis . The Trump team has also signaled, but not closed the deal, on the appointment of Adm. Michael Rogers as the director of national intelligence, the nation’s top spy.
And there has been little public discussion about who may head of the Department of Homeland Security, the top cabinet post charged with keeping the U.S. safe from domestic terrorist attacks.
Some members of the transition team were planning to pivot to economic policy appointments this week, focusing on such departments as Commerce and Treasury. But the internal debates will likely force Mr. Trump in the short term to keep his focus on his national-security team.
The process is expected to intensify on Monday, following Mr. Trump’s Sunday return from his Thanksgiving weekend at his Florida resort.
Former House Speaker Newt Gingrich, who backs former New York City Mayor Rudy Giuliani for secretary of state, said the search is playing out a bit like Mr. Trump’s longtime reality show, “The Apprentice,” as he publicly mulls the candidates’ skill sets and invites “audience participation.”
“It’s the only place so far that we have seen him trying to do an open apprenticeship, if you will,” Mr. Gingrich said.
Mr. Gingrich, who has ruled out serving officially in the incoming administration, said Mr. Trump may be looking at other contenders, and some conservatives have renewed a push for John Bolton, a former ambassador to the United Nations.
One conservative activist said he believes the choice has come down to Messrs. Romney and Bolton, while he said Sen. Bob Corker of Tennessee, chairman of the Foreign Relations Committee, remains a long shot for the job.
Picking Mr. Romney would make Trump look strong for standing up to the internal opposition, the activist said. Mr. Bolton would be well received by most of the GOP coalition, he added, although he could meet resistance on Capitol Hill, where Republican Sen. Rand Paul has expressed misgivings about his hawkish foreign-policy views.
This conservative added that Mr. Corker could be haunted by his work with Democratic nominee Hillary Clinton to secure the 2011 New Start Treaty, an agreement aimed in part at reducing the build-up of missiles and passed over conservative objections.
Mr. Corker has said he is gratified for the consideration, but he expects to remain in the Senate, while Mr. Giuliani and his allies have pressed his case for the State Department job.
Hogan Gidley, a Republican strategist who backed former Arkansas Gov. Mike Huckabee in the 2016 primaries, said Mr. Trump’s appointments thus far show a commitment “not just to diversity of race or gender, but a diversity of thought.”
“He’s not surrounding himself with a bunch of yes men,” Mr. Gidley said.
But Mr. Gidley said the Romney candidacy is tough to swallow given that the former Massachusetts governor went out of his way to oppose Mr. Trump during the GOP primary campaign. Mr. Romney said then that Mr. Trump posed a fundamental threat to American democracy, saying in one speech that “prospects for a safe and prosperous future are greatly diminished” if Republicans picked him as their nominee.
“It makes sense that some people in Trump-land would be concerned—and rightly so—about rewarding Mitt Romney’s hatred for Donald Trump with a cabinet position,” Mr. Gidley said.