There are many reasons for having breathing problems after heart surgery including build up of fluids around the heart or in the chest cavity or presence of too much fluid in the body which can be managed by draining the fluid off in addition of prescribing water pills.

Fluid accumulation in the lung, but also for the patient who have smoked a lot there would be a lot of secretions that develop in the lung because of mechanical respiration

Breathing problems can be common very early after heart surgery. The most common reason is some degree of fluid overload due to fluid shifts from the surgery or postoperatively. This can be treated with diuretics to help the kidneys remove excess fluid. Other causes can be excess fluid outside the lungs in the chest or around the heart which may need to be drained and can be detected by a chest Xray. An echocardiogram of the heart is very useful to determine heart function and to evaluate proper functioning of the cardiac structures as well.

Smoker, poor lung function prior to surgery, very long complicated operation where the breathing tube is not removed soon, pneumonia, heart failure, etc. -- a few reasons why one can develop breathing problems after surgery.

You should be examined by a Cardiologist and Pulmonary Physician.You may need to have Echo Cardiogram and Pulmonary Function test.It may be temporary but after these two tests are done you will find out the cause for your breathing difficulty.  

Breathing can be related to the amount of fluid in the lungs, which is related to how long you were on bypass, what medicine you are on,

Extra fluid you get during surgery leaks into the lungs. The fluid is necessary for your blood pressure at the time, but the body must remove it- urine must increase. That is why we give more medicine to make the patient pee after surgery.