I think it would depend on why they are procrastinating. As well as what types of things they typically putting off.

Are they lacking interest in the responsibility?
Was it thrust upon them rather than being of their own choosing to take it on?
How attached is their identity to the responsibility?
Do they lack general discipline?
Were they doing things they considered more important? What about more interesting to them?
Did they know how to do what needed to be done? Do they feel they have the knowledge and skill?
Are they under the age of 24?

From the description it could be weak Te, weak Se, and/or weak Ni.
Enneagram wise it could mean a super low score on e8 and/or e3.