For grammatical reasons, the verb choice for the first clause will influence the verb required in the second clause. Due to the use of the conditional "if" in the secondary (dependent) clause, the sentence can express one of two things: 1) a future possibility (one does not know the future), or 2) an unreal scenario (something that is not true).
In an unreal situation, we might have a sentence like this:
- I would see a doctor if I were you.
Naturally, I am not you, nor could I be you--so this is an unreal scenario.
Because English has no dedicated subjunctive form, verbs are changed to their past tense fill this role. To express something unreal, we use this past tense. Note that in American English, the unreal past tense of "to be" must always be "were", whereas in British English "was" is also in use.
In the example of the question, two forms are possible.
- I will be surprised if I do not complete it by the end of the day today.
Unreal Future Tense
- I would be surprised if I did not complete it by the end of the day today.
Technically, because this is future, the speaker cannot know the outcome with certainty. Placing it in the future tense simply shows that the speaker thinks the task will be accomplished, and will be surprised otherwise; whereas placing it in the unreal future tense shows that the speaker regards the failure to accomplish the task as highly improbable--to the point of being considered an unreal scenario.
In other words, the two options express varying degrees of certainty for the same outcome. Saying "will be surprised if" indicates that one might be surprised, depending on what happens; saying "would be surprised if" indicates that one does not expect this surprise to become a reality.