Hamilton stands on the brink of being beaten by a team-mate for the first time in his Formula One career, with the 26-year-old trailing his fellow Briton by 38 points with just 50 more available.
Such a statistic would merely rub salt into Hamilton's wounds given it has been a year to forget both on and off track, with incidents and penalties hurting as much as his recent break-up with pop star Nicole Scherzinger.
In Sunday's Indian Grand Prix, Hamilton was involved in a sixth collision with Ferrari's Felipe Massa, before eventually trundling home a disappointing seventh.
In contrast, Button went on to secure the runner-up spot behind a perfect performance from Sebastian Vettel who, for the first time in his career, achieved pole, win, and fastest lap, as well as leading for every lap.
In the last seven races Button has now finished ahead of Hamilton on six occasions, with the strain perhaps showing on the part of the latter.
"In truth Lewis will be feeling under pressure because of the great performance of Jenson at the moment," said Whitmarsh.
"If you're honest, the first driver you want to beat is your team-mate. We don't hide from that, and neither do Lewis or Jenson.
"They are there to beat each other, but Jenson's been on a run.
"Of course, Lewis is the great exciting driver he is, but he'll not like being beaten by anyone, least of all by Jenson.
"Even though outside the car they have a fantastic relationship, Lewis will not like being beaten by his team-mate.
"But then I don't want him to enjoy being beaten by his team-mate. I want him to try and beat Jenson, just as I want Jenson to beat Lewis."
One area of concern for Whitmarsh, though, is Hamilton's currently self-critical nature in which he is constantly beating himself up.
It was the same on Sunday as Hamilton apologised profusely to the team, primarily for what he feels is "the negativity" that surrounds him, even though he was not at fault for the latest incident with Massa.
Asked whether he thinks Hamilton is too hard on himself, Whitmarsh replied: "Yes I do, frankly.
"I've told him on several occasions - 'Don't apologise. You're a racing driver, and if you've made a mistake accept it, learn from it and move on'.
"But he's very analytical. He's very serious about trying to do the best job he can.
"I've known Lewis for a long, long time and he's been like it since he was a kartist and he beat up on himself.
"That's his way, his psychology. That's how he motivates himself."
After his sour demeanour in Korea, when his split with Scherzinger was hurting the most despite claiming his first pole for 27 races and finishing second, Whitmarsh believed he saw an improvement in Hamilton's body language over the weekend.
Sadly, it never materialised into the overall performance that was required, with Whitmarsh adding: "I thought that a good race here would allow him to build.
"But he still has all the skills. We saw him qualify and race fantastically in Korea and we saw him qualify fantastically here, so it could change.
"It hasn't changed quickly enough for him or I or anyone of us, but it could change and he could have a brilliant drive in Abu Dhabi, and we then move on to a different story."
As a neutral observer, F1 supremo Bernie Ecclestone feels Hamilton is enduring a dip he will ultimately pull himself out of.
"It's not intentional is it?" remarked Ecclestone on the number of incidents between Hamilton and Massa.
"These things happen. It's just strange it always happens to those two.
"But in life you go through ups and downs. He is just going through a bit of a rough period generally in his life.
"When life is easy you get lucky and everything goes well, but when things start going wrong they always seem to pile up.
"But he'll get out of it. I spoke to him on Saturday and he was all right. I'm sure he'll be okay."