Cambiar la fecha no debería suponer tanto trabajo.

Yes. In Spanish, an infinitive can act like a noun phrase and be the subject of a sentence.

So Cambiar la fecha means changing the date or to change the date as an idea.

• Cambiar la fecha no debería suponer tanto trabajo.
• Literally: Changing the date should not involve so much work.

This is very common in Spanish:

• Fumar es malo. = Smoking is bad.
• Viajar solo da miedo. = Travelling alone is scary.

So the subject here is the whole phrase cambiar la fecha.

Both are possible, but they sound slightly different.

• Cambiar la fecha focuses on the action itself: changing the date
• El cambio de fecha turns it into a noun phrase: the date change or the changing of the date

So:

• Cambiar la fecha no debería suponer tanto trabajo sounds natural and direct.
• El cambio de fecha no debería suponer tanto trabajo is also correct, but a bit more nominal and formal in tone.

Spanish often likes the infinitive for general actions.

Here debería means should or ought to.

So no debería means shouldn’t.

It expresses expectation or opinion, not a strict command. The speaker is saying that, in their view, this action is not expected to be so difficult.

Compare:

• No debe suponer tanto trabajo = It mustn’t / it should not involve so much work
  This can sound stronger or more categorical.
• No debería suponer tanto trabajo = It shouldn’t involve so much work
  This sounds softer and more natural in many situations.

Because the subject is the whole infinitive phrase cambiar la fecha, and Spanish treats that as singular.

So the verb agrees with that singular idea:

• Cambiar la fecha no debería...
• Viajar solo es...
• Comer tarde me sienta mal.

Even though the action may involve many people, the grammatical subject is still one thing: the act of changing the date.

This is a very common learner question because suponer can be a false friend.

Here suponer does not mean to suppose in the English sense of to guess/assume.

In this sentence, suponer means:

• to involve
• to entail
• to mean
• to represent

So no debería suponer tanto trabajo means something like:

• shouldn’t involve so much work
• shouldn’t be so much work
• shouldn’t entail so much effort

This use of suponer is very common in Spanish.

Because deber works like a modal verb here and is followed directly by an infinitive.

Structure:

• deber + infinitive

So:

• debería suponer
• debe venir
• deberíamos salir

You do not say debería que suponer.

This is similar to English should involve, not should that involve.

Because tanto is used before nouns, while tan is used before adjectives or adverbs.

Here trabajo is a noun, so you need tanto:

• tanto trabajo = so much work

Compare:

• tanto trabajo = noun
• tan difícil = adjective
• tan rápido = adverb

So:

• No debería suponer tanto trabajo. = correct
• No debería suponer tan trabajo. = incorrect

Here trabajo is being used as an uncountable noun meaning work or effort, not a job.

So:

• trabajo = work, effort
• un trabajo = a job / an assignment / a piece of work

In tanto trabajo, the meaning is abstract and uncountable, so singular with no article is normal:

• Tengo mucho trabajo.
• Eso da bastante trabajo.
• No debería suponer tanto trabajo.

Yes, but the nuance changes a little.

• mucho trabajo = a lot of work
• tanto trabajo = so much work / that much work

Tanto often sounds a bit more emphatic, especially when the speaker feels the amount is excessive or surprising.

So:

• No debería suponer mucho trabajo = more neutral
• No debería suponer tanto trabajo = more expressive, like it really shouldn’t be this much work

Because Spanish does not need a dummy subject like English it in this kind of sentence.

English often says:

• It shouldn’t be so much work to change the date.

Spanish instead uses the real subject directly:

• Cambiar la fecha no debería suponer tanto trabajo.

So the sentence is built around the action itself, not around a placeholder subject.

Spanish can sometimes rearrange the sentence in a way that feels closer to English, but it still does not need a dummy it.

Yes. A common alternative is:

• No debería suponer tanto trabajo cambiar la fecha.

This is also correct and natural.

The difference is mostly about focus:

• Cambiar la fecha no debería suponer tanto trabajo.
  Starts by highlighting the action changing the date
• No debería suponer tanto trabajo cambiar la fecha.
  Starts with the opinion/judgment it shouldn’t involve so much work

Both are good Spanish.

Not exactly.

• cambiar la fecha = to change the date
• cambiar de fecha = to change date / to be moved to another date

With events, cambiar de fecha often sounds a bit more like to be rescheduled or to move to a different date.

Examples:

• Tenemos que cambiar la fecha de la reunión.
  = We have to change the date of the meeting.
• La reunión ha cambiado de fecha.
  = The meeting has been moved to another date.

In your sentence, cambiar la fecha is the most straightforward choice.

Yes, it is natural in Spain.

It sounds neutral and idiomatic. A Spaniard might also say:

• Cambiar la fecha no debería dar tanto trabajo.
• Cambiar la fecha no debería costar tanto.
• No debería ser tan complicado cambiar la fecha.

But no debería suponer tanto trabajo is perfectly good Spanish, especially if you want a slightly more formal or polished tone.