This is my first time answering a Yahoo question, but to me it's a simple answer... Assuming your target BS = 100, then you were 100-61 = 39 mg/DL below your target. If 1g of CHO (Carbohydrate) raised your BS by 4 points, then you would need to eat 39/4= 10g of CHO w/o insulin in order to RAISE YOUR BS to proper target level.
At this point, you could eat your breakfast AND take your 12units and if the dosage was correct, you should be at 100mg/DL (where you started) 2 hours after you finish eating (known as "post-prandial" blood sugar test).
If I were at 61mg/dl before a meal, then I would drink 1/3-1/2 glass of fresh Orange juice, then start eating breakfast. After about 10-15 minutes, I would THEN take my "pre-breakfast" insulin shot (12 units?).
THE TIMING IS IMPORTANT, since your "normal routine" assumes that you are at your "target range" AT THE TIME you take your insulin. If your BS=61 and you take more insulin, then your BS is nearly guaranteed to drop LOWER. If you got distracted or failed to eat something within 5-10 min then you risk going hypoglycemic, passing out, and entering comatose state since you've got 12units of fresh insulin "on board". BAD news. All of this can happen in 10-30 minutes depending upon the type of insulin you take.
By eating first, and THEN taking your insulin, at least you've given your body a head start digesting the food. Depending upon the type of breakfast you eat, it may take 30-60 minutes to get into your blood stream and raise your BS (thus the OJ suggestion). 1/3 cup of fresh OJ is roughly 10g of FAST acting Carbohydrates. My guess is OJ would raise BS from 61 -> 100 in approx. 5 minutes. To be on safe-side, I'd drink 1/2 cup of OJ because I'd rather be slightly higher than target than slightly lower than target.
BTW, all of the calculations above were based on values for an "average male adult". Actual numbers should be known per each diabetic and may vary slightly from those used in the above example.
Of course all of this should be discussed with your doctor, etc.