"It is Tuesday today."
It sounds very unnatural.
In the English sentence, «it» is a dummy pronoun. It doesn't refer to anything in particular.
- It is a cat. — 'it' refers to the cat, it references something in real life (we could replace it with some noun: 'The animal is a cat'). Here, 'it' is a normal pronoun.
- It is Tuesday. — 'it' doesn't refer to anything (there is no thing it references, we can't replace it with anything; it's there just because 'Tuesday is' is ungrammatical in English). Here, 'it' is a dummy pronoun.
Ukrainian doesn't use dummy pronouns. «Це» is only used when it's a normal pronoun referencing something.
Technically you could make up a context when 'It is Tuesday today' is not a dummy pronoun (e.g. I've decided to learn one word every day. It is Tuesday today. — here, 'it' refers to 'word', 'Today, the word of the day is Tuesday' — in this context it could be translated «Це вівторок сьогодні»), but such contexts are very rare.
Sorry, I don't understand your question. The sentence "It is Tuesday today" has no objects.