Unlikely. It would be political suicide for a house Republican to cross Trump at this juncture.

Not the House - the Senate. It would not be shocking for a few Senators to vote against Gaetz, given his lack of legal and/or executive experience and his....demeanor. If RFK, Jr. gets named for HHS I can see him having some problems as well.

Hegseth will be closely vetted - not because he's necessarily objectionable in terms of his policies or positions, but because there's quite a few GOP Senators who care an awful lot about the military and are going to take a very close look at whether they think he's up to the job of running that organization. Unlike Gaetz or RFK, Jr., I think all of those Senators might be open to him having the job - but he's someone whose nomination can rise or fall depending on whether the GOP Senators think he's capable or not.