You might have high blood pressure in the morning for reasons beside your medicine. Overuse of alcohol can raise blood pressure. So if you do drink alcohol, keep it to no more than a couple of drinks per day. One drink means 12 ounces of beer, 8 ounces of wine, or one shot of hard liquor.. Sleep apnea is another cause of high blood pressure early in the morning. With sleep apnea, the airway becomes blocked or breathing muscles stop moving. Breathing temporarily stops or becomes shallower. This can happen hundreds of times each night.