It would be no surprise though, if Rugby Football Union chief executive Francis Baron and elite rugby director Rob Andrew also wanted a word as England find themselves reeling from seven successive losses.
Eight defeats on the bounce would represent an unprecedented figure for England since they began playing international rugby 135 years ago.
And how much longer Robinson, who has won just eight of his 20 Tests in charge, remains at the helm is now a source for animated debate.
Many pundits, including prominent ex-England players, have called in no uncertain terms for an immediate resignation.
But Robinson, it would appear, intends soldiering on as an autumn series that has already assumed nightmare status concludes with back-to-back clashes against the Springboks.
"I have got to accept that was a poor England performance, but it's not me splitting," said Robinson.
"We are a team together, and we all have a part to play in this.
"I am in charge of the England team, and that remains unchanged. This is my lowest point as England coach. I will be preparing the side for the South Africa game and won't be discussing anything until Monday."
Robinson's anger with his team could be gauged through numerous second-half substitutions, which included taking off half-backs Charlie Hodgson and Shaun Perry with almost a third of the contest still remaining.
"It is disappointing for Charlie, and it is disappointing for Shaun, but we felt - and we discussed it for five or six minutes - that those were the right calls to make," added Robinson.
"I have watched the game and I will review it, and I back our judgement that those were the right calls to make."
Injuries permitting, Robinson must surely contemplate making up to 10 changes, with Mark Cueto, Mathew Tait, Josh Lewsey, Andy Goode, Peter Richards, Andrew Sheridan, Steve Thompson, Phil Vickery, Chris Jones and Tom Rees all pressing claims ahead of a likely team announcement Tuesday afternoon.
Hooker George Chuter, one of several players who could lose his place, said: "A lot of what we've done has been good - it's just getting it off the training field and on to the playing field.
"I think people are entitled to their own opinion (England were booed off by a 74,000 crowd). They pay their money, they can do what they like at the end of the game.
"It is disappointing, because it is not as if we are not trying. Everyone did their best, but things didn't come off.
"Our commitment and endeavour was there, it is just a matter of getting our skills and accuracy up to speed. There is a huge amount of room for improvement, and we have got to keep working - we are not a million miles away.
"We've lost seven in a row, and it is demoralising, but it only takes a couple of bounces of the ball to change your luck, and things can easily turn around."
For the record, Argentina's first Twickenham triumph in four attempts was inspired by 22 points from substitute Federico Todeschini.
It was the Pumas' day, but England's staggering level of incompetence ensured they commanded every headline.