Senior ministers are "absolutely furious" about his resignation and departure from government.
Some ministers believe the claims in his letter are "just not true because he is well aware that the welfare changes have always clearly been about saving money as well as improving the systems".
It's suggested that his central motivation is the EU referendum, and, for others who are supporting him, a strategy to kill off George Osborne's hope of taking over from David Cameron.
IDS's team is adamant that his exit is entirely about the handling of PIPs (Personal Independence Payments) and nothing to do with the EU.
Whatever the truth, it is very dangerous for a political party to be so publicly divided, and, on a very simple level, for its members to be so angry with each other.

Small studies by UK and Korean scientists indicated patients were less likely to fixate on food and body image after a dose of oxytocin.
About one in every 150 teenage girls in the UK are affected by the condition.
The eating disorders charity Beat said the finding was a long way from becoming a useable treatment.
Oxytocin is a hormone released naturally during bonding, including sex, childbirth and breastfeeding.
It has already been suggested as a treatment for a range of psychiatric disorders, and has been shown to help lower social anxiety in people with autism.
And one four-week study in Australia found people given doses of oxytocin had reduced weight and shape concerns.
In the first of the most recent studies, published in Psychoneuroendocrinology, 31 patients with anorexia and 33 people who did not have the condition were given either a dose of oxytocin, delivered via nasal spray, or a placebo, or dummy, treatment.
They then looked at a series of images to do with a range high and low calorie foods and people of different body shapes and weight.
People with anorexia have previously been found to focus for longer on images of overweight people and what they perceive as undesirable body shapes.
However after taking oxytocin, patients with anorexia were less likely to focus on such "negative" images of food and fat body parts.
The second study, published in PLOS ONE, involved the same people and looked at their reactions to facial expressions, such as anger, disgust or happiness.
It has been suggested that anorexia can be linked to a heightened perception of threat, and animal research has shown oxytocin treatment lessened the amount of attention paid to threatening facial expressions.
In this study, patients with anorexia were less likely to focus on the "disgust" faces after oxytocin treatment.
They were also less likely to avoid looking at angry faces.
Eating disorder expert Prof Janet Treasure, from King's College London's Institute of Psychiatry, led both studies.
She said: "This is early stage research with a small number of participants, but it's hugely exciting to see the potential this treatment could have.
"We need much larger trials, on more diverse populations, before we can start to make a difference to how patients are treated."
Her co-researcher, Prof Youl-Ri Kim, from Inje University in Seoul, South Korea, added: "Our research shows that oxytocin reduces patients' unconscious tendencies to focus on food, body shape, and negative emotions such as disgust.
"There is currently a lack of effective pharmacological treatments for anorexia.
"Our research adds important evidence to the increasing literature on oxytocin treatments for mental illnesses, and hints at the advent of a novel, ground-breaking treatment option for patients with anorexia."
Leanne Thorndyke, of the eating disorders charity Beat, said: "Eating disorders are complex, and a number of risk factors need to combine to increase the likelihood that any one individual develops the condition.
"Brain chemistry and hormonal factors are part of the mix, with adrenaline, dopamine and the various appetite regulating hormones such as ghrelin being active areas for researchers as well as this research looking at the hormone oxytocin.
"We know that there is much that still needs to be understood about the biological basis for eating disorders.
"We are hopeful that this research will lead to a new, effective treatments being designed, but it is early days yet."
It's not just Iain Duncan Smith who's angry.
[NEXT_CONCEPT]
A hormone released during childbirth and sex could be used as a treatment for the eating disorder anorexia nervosa, scientists suggest.