I agree with what Srikanth has to say. At times we are inclined to take up additional tasks with the intention that it gets recognized by the management. However once you take up the tasks it is considered by the management that you will fulfill the task along with the deadline that you have on your other tasks. So my advise is take up the new tasks only if you have completed your existing tasks. The industry only values specialization. The management will not give you additional time thinking that you have a learning curve to go through. If a designer has left the team then it is the headache of the management team to find a new resource.
I have myself experienced at times that we tried to take up additional tasks with the intention of impressing the management. If the task get completed then it is ok but if the project misses the deadline then you will be one of the scape goats to be blamed for project delays.
Web designing is a specialized skill and a different area so don't try to dilute your focus on your main skill by trying to learn a new skill that doesn't complement your main skill.