The threat comes from Liam Byrne, the Cabinet Office minister, who would like COI to promote the Government's anti-recession measures in an umbrella campaign.
The Government would doubtless argue that desperate times call for desperate measures. The International Monetary Fund warns that Britain will be hit harder than any other advanced nation in the worst recession for more than 60 years. Isn't it reasonable to provide some reassurance by telling people what the Government is doing about it?
Well, such an initiative may well be open to question. Assuring the public that the Government is taking the right action to steer the UK through the crisis isn't the same as encouraging them to eat healthily or drive more carefully.
The country's exposure to the global slump - and the degree to which Gordon Brown is culpable - is a hugely contentious and divisive issue. And one that might decide the outcome of the next General Election.
Issues like this are a perpetual dilemma for COI. Any message involving health spending or education runs the risk of being politically contentious.
Alan Bishop, COI's outgoing chief executive, makes the valid point that much legislation is politically motivated, but once it becomes law, it is COI's job to communicate it as well as it can. However, whether a campaign publicising measures that may determine whether or not Labour stays in office is valid under those terms is highly debatable.
Should the Government press ahead, it risks stepping on a slippery slope - and COI needs to tell it so.