Hell Steve... if it's the delta that's important, mine will have to be close stopping to indicate I've got really fit 
When you say 'first thing in the morning' - Do you mean like FIRST thing. whilst lying in bed and barely having moved?
Having written the above sentence, I just did an experiment. I had my laptop on lap, sat up with legs up on the sofa. Heart rate 38. I just moved a little, to put my feet on the floor, still sat down. I measured 40. I slowly stood up, and waited quietly for a minute - then measured 47. Then lay down flat on the floor, waited a minute, and it was back down at 41.
From this (not very scientific) experiment, I'd suggest that HR is affected a lot by whether or not your heart has to fight gravity, to get blood to and from your extremities. The last reading (laid flat) should theoretically have been the lowest, but could be within normal scatter of results or (likely) affected by me not resting long enough after getting myself in position.
So measuring just after you've got up, could give a very different result than if you measure just before you get up.