After the phenomenal success of Alec Baldwin and Melissa McCarthy on Saturday Night Live, celebrities are clamouring to spoof the Trump team on the sketch show.

On Monday, Zach Braff became the latest to put his hand up for a shot on the long-running comedy show, which saw its ratings sky-rocket on Saturday, reported Entertainment Weekly.

Braff has volunteered - begged - to play White House senior policy advisor Stephen Miller, who was criticised earlier this week for his interviews defending President Donald Trump's claim of widespread voter fraud.

Others who have expressed keen interest in impersonating the new administration include Kathy Griffin, who is vying with Braff for the Miller role; Christine Baranski for Secretary of Education Betsy DeVos and Rosie O'Donnell for counsellor Steve Bannon.

Bannon is now played by the Grim Reaper on the show, but O'Donnell is so keen that she even launched a hashtag, #BannoninChief and changed her Twitter profile picture to a mash-up image of her and Bannon.

Baldwin's younger brother Billy jokingly told Access Hollywood that he would play Trump's son, Eric, because it was easy.

"I've got the slicked-back hair. I'm a little too old for that, but yeah. Because I just have to sit there and go, 'Duh'," he said.

Alec Baldwin's impersonation of Trump and McCarthy's take on White House press secretary have won rave reviews, but brickbats from the real president and press chief themselves.