Flynn has drawn criticism for calling Islam "a political ideology" and ex-colleagues have said they are worried about his volatile temperament.
These Republicans see an historical analogy in the Ronald Reagan administration.
Reagan's first White House chief of staff, James Baker, and his deputy, Mike Deaver, ran circles around Reagan's right-wing lieutenants led by Ed Meese. Later, Secretary of State George Shultz, with a key ally, first lady Nancy Reagan, set the foreign policy agenda over the objections of hawks like National Security Adviser William Clark.
But Trump is not Reagan.
Unlike his Republican predecessor, the President-elect is a man of few convictions and little interest in policy specifics. It's not clear who has his ear or how he'll resolve disagreements among his advisers.
But Pence, Ryan and Priebus have worked together and share mutual respect.
Priebus lacks Baker's command of politics and policy. But he's shrewd enough and already is placing key people in White House positions, a step towards exercising power that seems of little interest to Bannon.
The conservative establishment agenda includes deregulation, big tax and spending cuts, a reasonably ambitious infrastructure plan that doesn't bust the budget and a replacement for Obamacare that doesn't take effect for several years. They also hope to avoid aggravating racial divisions and to work around Trump's campaign promise to deport millions of undocumented foreigners.
Ryan and his allies may try to find common ground with some Democrats on a few issues, even if doing so inflames the hard right in the administration and in Congress.
On national security, much of the Republican establishment disdains Flynn, a once-respected tactical commander in Afghanistan who now seems consumed with a bitter hatred of the Obama administration. It fired him from his post as head of the Defence Intelligence Agency. He is virulently anti-Muslim and friendly to Russia.
There is a sense now that Mattis - who has one more star than Flynn - will prove more capable and that Tillerson, if confirmed, is likely to become an ally of the defence chief.
Tillerson will face a rough confirmation process because of his friendly relationship to Russian dictator Vladimir Putin.
He almost certainly will have to articulate a distinction between his role doing business as CEO of Exxon-Mobil and being America's top diplomat. He will probably be opposed by most, if not all, Democrats, so his fate could rest with anti-Putin Republican senators like John McCain and Lindsey Graham.
The anti-establishment Trump camp already is pushing back. Trump's advisers, wrote Ann Coulter, a strident right-winger and Trump champion, "include just the type of Republicans whose second-tier law schools make them particularly susceptible to the cheap respectability of establishment media approval."
- Bloomberg