这里的 a great deal of 跟 a great deal of time / money(大量的时间/钱)等不是一个用法。你的句子涉及 ask sth of sb(向某人某求某物)。如:
Can I ask a favour of you? 能请你帮个忙吗?
You're asking too much of him. 你对他要求过分了。
You have no right to ask anything of me. 你没有权利对我提要求。
你的句子的意思:
The job asks a great deal of me.
这个工作要求我付出很多。