There is no pressure on the lead rope. The horse is standing still so should not be feeling any pressure.
This is the most common thing that I see - a horse standing quietly (either in a halter on the ground or in a bridle under saddle) and still being held under constant pressure. Unfortunately this desensitises the horse to the pressure so it soon becomes meaningless and you need increasing amounts of pressure to get your horse to react or change his behaviour. Try to think of pressure (rein, lead rope, hand, leg, whip, lariat, emotional, body language and so on) as asking for a change - when you get the change that you asked for, release the pressure. The key thing here, of course, is getting the change that you asked for. You need to know what it is that you want the horse to change or move so that you can release when he does. If you sit on your horse and have a conversation with a friend while holding (even slight) pressure on the reins, then you must expect he will either jig about trying to find the right answer or become 'deadened' to the pressure and require significantly more to get a change in behaviour. What other quick un-training methods do you see a lot?