"I have a lot of work to do, but I want to do it."  (slightly odd in terms of the logic)

=> 해야 할 일이 너무 많지만, 그래도 할 거야.  

Compare it with these others with a different main clause.

"I have a lot of work to do, so I have to start doing it right away."

=> 해야 할 일이 너무 많아서, 빨리 시작해야 돼.해

"I have a lot of work to do, but I don't want to do it."

=> 해야 할 일은 너무 많지만, 하기가 싫어.