Could you please tell me what is the difference between two phrases?
Everything needs doing exactly today.
Everything is to be done exactly today.
1. Everything needs doing today = Everything is to be done today. (Basically the same)
2. Everything has to be done today = Everything must be done today. These statements are stronger.
3. Everything definitely needs doing today. This has the stronger force of 2.
Your original sentences mean "Everything we do today must be done exactly (precisely, correctly)". It doesn't mean 3.