Well, I'm going to wade in here and call a spade a spade. Hard, infrequent and difficult to pass jobbies are a common problem in many people.
It does indeed occur in people who low carb but the people who mention it the most are folks who have started on the Atkins diet at the induction phase. My guess is that the transition is too much change at once for their guts to cope with. Also, many newcomers are a bit hesitant to eat as much fat as is necessary and may get cramps / wind from eating the four portions of vegetables a day.
My suggestions are:
Adjust your diet downwards gradually
Eat plenty of low carb veg
Put lots of butter on them
drink plenty of water
if necessary add a fibre supplement and / or take senna 7.5-15mg at night for a while.
Personally I have looser bm than I did prior to going on Atkins. I do eat loads of fat. This stimulates cholecystokinin which speeds up your gut transition time (peristalsis) and improves satiety. I also eat loads of seafood. You can't beat a big bowl of mussels ! (probably for the wrong reasons !)
I wouldn't let a bit of constipation that can be easily managed get in the way of having normal blood sugars.