The expression for obligation and necessity for both PRESENT and FUTURE is "Have to".
The difference between them, for clarification purpose or for avoiding confusion, is the time expression.
- I have to finish this job now. -- Present
- I have to finish this job by next Saturday. -- Future
However, the obligation in both cases exists at the speaking moment, even if one of them will be accomplished in the future time.
On the other hand, "Will have to" is the expression for obligation and necessity used with a conditional structure "Future Possible".
If my boss calls me tonight, I will have to work (tomorrow).
In the sentence above, the obligation for working tomorrow DOES NOT exist at the speaking moment; the obligation will be in force only if the condition if my boss calls me... becomes true. This means that there is no present obligation.