In our outcome/achievement orientated society we can measure our faith by the 'things' we do for God. Sometimes it feels like we are only pleasing God if we are 'doing' something worthy. This is especially true in Christian ministry. In some circles we boast about 'busy-ness', albeit in a sheepish way. (Our discomfort is more with the posture of boasting rather than being uncomfortable with being too busy.) I have noticed, myself, that when people ask how our church/ministry is going that I want to demonstrate to other Christians the worthy things that we are doing or achieving.
I don't think it is wrong to be busy at times. There will always be times when things pile up on us and different things demand our attention at the same time. The danger comes when we only know how to be busy. When we maintain a roll of busy-ness out of habit it can lead to a lack of skill in discerning what is really important to spend time and energy on. More importantly, it demonstrates to the people around us that we believe personal worth is in achievement rather than in being a beloved child of God.
So often, when busy, we come to trust in our own efforts. We can become proud of what we see as our own achievements as a busy and important person. We can come to think that God will only really love us if we are doing something for him. It is sad that we can sell our loving father so short, that we see his love with worldly eyes, contingent on us being good or worthwhile.
God loves us in our lostness and failure. His grace is that he comes to us and loves us before we can do anything for him. This grace then leads to gratitude in us and a desire to be part of his mission to the world, but the grace comes first.
This must be balanced with a desire to live a holy, godly life and to be involved in labour that will withstand the fire of judgement. God wants us to live a fulfilled life* - I would suggest, a balanced life - where we understand the value of work and service but also know the relief of rest and the joy of celebration. The work God does in our lives and spirits is a much truer mark of value than our own work and achievements.
*John 10:10 - 'I have come that they may have life, and have it to the full.'
It is interesting that Jesus talks about bringing life for people 'to the full' in the context of his shepherding and his sacrifice. The full life is found in following the shepherd and living in his care.