But they should be very, very careful about what action they decide to take because this is more than just about Armstrong, much more.
Earlier today the Executive Board suspended the Indian Olympic Association (IOA) for failing to hold its forthcoming elections under the rules of the Olympic Charter.
In the great robbery that was Armstrong's career, getting away with a bronze medal barely mentions a footnote on the charge sheet when set against stealing seven Tour de France titles. But, like everyone else, so upset are the IOC that they were taken for a ride - literally - by the American that they seem prepared to try to find a way to circumnavigate their own rules to take it away from him.
John Coates, the Australian lawyer who is a member of the IOC Executive Board, claims that the statute "simply doesn't apply if you have broken the law". That seems a fair enough argument but, while Armstrong may have been tried and found guilty in the court of public opinion, he hasn't actually been convicted of anything criminal (although he may still face perjury charges at some point in the distant future).
Thomas Bach, meanwhile, another lawyer, who is in pole position to replace Jacques Rogge as President of the IOC, claims that they must strip Armstrong of the medal because they have a "zero-tolerance policy on doping".
Well, if that's the case, and they are going to be consistent, then the IOC had better book a meeting room in the Palace Hotel in Lausanne on a long-term basis, get their most recent copy of The Complete Book of the Olympics by David Wallechinsky off the shelf, take the tops off their red pens and start revising because this could take some time...
Where shall we start?
I know, how about the time trial from the Sydney Olympics in 2000? Yes, the very same race that Armstrong finished third in and which the IOC are so keen to revise the result for. Because there, in second place, just one spot ahead of Lance was Jan Ullrich, his old German rival, who claimed the silver medal to add to the gold he had won earlier in the Games in the road race.
Like Armstrong, right to the time he got off his bike and hung up his helmet, he denied doping, although there was plenty of circumstantial evidence for which you hardly needed to be Hercule Poirot to have your suspicions aroused even before he was found guilty of a historic doping offence earlier this year, despite having retired in 2007.
That was even before Ullrich's old boss at Telekom, Rudy Pevenage, admitted in the wake of the Armstrong scandal that they had doped. The IOC has already investigated Ullrich once but decided that there was nothing they could do because the statute of limitations had expired (even though they are prepared to overlook that in the case of Armstrong).
Okay, there is a grey area here because Pevenage has claimed that Ullrich was "clean" between 1998 - when the Festina scandal erupted - and 2001 when they realised their US rival "had become superhuman...and we tried to find the recipe, the same recipe as Armstrong". But is there anyone out there who truly believes that Ullrich is more deserving of being allowed to keep his medals from Sydney than Armstrong? I think not.
How about another case, that of the British runner Mike McLeod. He crossed the line third in the 10,000 metres at the 1984 Olympics in Los Angeles but was promoted after Finnish rival Matti Vainio, who finished second, was disqualified for failing a drugs test for anabolic steroids, the first track and field medal winner to be disqualified at an Olympic Games.
Then, several years later, the Italian gold medallist Alberto Cova, confessed to blood doping, a process where blood is taken from the athlete, stored while the body replenishes itself, then given back prior to competition. The procedure was sanctioned by the Italian athletics federation at the time but was not technically illegal because of a loophole in the rules, so another grey area the IOC will argue.
But, let's call a spade a spade here, it was cheating and if the IOC are to embrace this new policy of "zero tolerance" however much time has elapsed, then surely there is a 60-year-old grandfather in Newcastle who deserves to be given the gold medal he was cheated out nearly 30 years ago?
Okay, I can see that this isn't as easy as it looks. So how about a case where there is no doubt, where the athlete themselves have admitted that they were doped when they won their gold medal and have even asked the authorities to strip them of their performances? We can't get any more clear-cut than that, can we? They have even looked their beaten opponent in the eye and admitted that they cheated.
Step forward Petra Schneider, the East German swimmer who won the 400m medley at Moscow in 1980. She has subsequently acknowledged that she was fuelled throughout her career by anabolic steroids prescribed to her by the East German authorities. So honest was she that when she met Sharron Davies, the Briton she beat in the Soviet capital, for a television programme she admitted it on camera.
After the fall of the Berlin Wall in 1989, hundreds of thousands of pages of documentary evidence was uncovered of a state-administered drugs programme involving leading athletes, like Schneider, who could be identified by codes or in some cases letters kept in Stasi files. They are the "War and Peace" of doping history and make the 1,000 page document prepared by the United States Anti-Doping Agency (USADA) on the Armstrong case look like an Enid Blyton paperback.
Besides Schneider, those named in public include track and field Olympic champions Marita Koch, Barbel Wockel, Heike Drechsler, Jürgen Schult and Thomas Munkelt.Yet, look at the results from when GDR made their Olympic debut at Mexico City in 1968 until Seoul 1988, which marked their final appearance, their names are all still there, including Schneider.
The United States Olympic Committee asked for the redistribution of gold medals won at Montreal in 1976 after Andrea Pollack, a swimmer who won two gold medals there, admitted she had been doped at the time. But, despite court rulings in Germany that substantiate claims of systematic doping, the IOC Executive Board has always resisted revising the results.
In turning down the American petition on behalf of its women's medley relay team in Montreal and a similar petition from the British Olympic Association on behalf of Davies, the IOC has always made it clear that it wanted to discourage any such appeals in the future.
Even if Armstrong is stripped of his medal tomorrow the IOC apparently plan to leave the third place position vacant rather than redistributing it to the fourth-placed Abraham Olano Manzano from Spain. That is following the lead of the International Cycling Union (UCI), who have declined to reallocate any of Arrmsong's seven Tour de France victories between 1999 and 2005, perhaps mindful that in three of those years Ullrich had finished second to him.
There is a precedent for an Olympic "ghost" race, of course. Three years ago, at the corresponding IOC Executive Board meeting, they took away the five medals, four of them gold, American Marion Jones had won at Sydney, the end of a long running saga that had started when she was still covered by the IOC's statute of limitations following her admission that she had been using drugs at the time.
The medals they took away included the gold in the 100m, which they declined to re-award to the runner-up Ekaterina Thanou, the Greek who herself has been banned for being linked to drugs. That decision by the IOC was perhaps perfectly understandable given the circumstances.
But, if they decide to take action against Armstrong tomorrow even though it would clearly be illegal under the rules of the Olympic Charter and strip him of his medal (good luck getting him to package it up and post it back to Lausanne, by the way), they could stand accused of victimisation. I, though prefer to think that Armstrong is more suffering from his cause célèbre (although I have no sympathy for him).
It is unlikely that the IOC would have been as tough on, say for example, an Eastern European weightlifter from Sydney who had been exposed as a drugs cheat a dozen years later because such a case would have warranted just a few lines in the media. Then they would have hid behind the Olympic Charter and the "statute of limitations".
Armstrong doesn't deserve to keep his bronze medal but nor do the likes of Davies deserve the injustice of seeing the IOC ignore the statute of limitations that were used to deny them the justice they craved just because they need to be seen to be tough now.
Duncan Mackay is the award winning editor of insidethegames. A former UK Sports Journalist of the Year and UK Sports Internet Writer of the Year, he previously worked for The Guardian and The Observer.