Vi har kun lidt tid i dag.

In Danish, have is have, and its present-tense form is har:

• at have = to have
• jeg har = I have
• vi har = we have

So Vi har simply means we have.

By contrast, er is a form of at være = to be, so Vi er means we are, not we have.

Kun means only.

In Vi har kun lidt tid i dag, it limits the amount of time: we only have a little time today.

Its position is very natural here because it comes before the part it affects:

• kun lidt tid = only a little time

If you move kun, the emphasis can change. In this sentence, placing it before lidt tid clearly shows that the limited thing is the amount of time.

Lidt means a little / a small amount of, and it is the normal choice with uncountable nouns like tid (time).

So:

• lidt tid = a little time / not much time

Tid is usually treated as something you measure, not count as individual items, so lidt fits well.

En lille tid is not the normal way to say this. Lille means small/little as an adjective, but with time in this meaning, Danish normally uses lidt.

Compare:

• lidt vand = a little water
• lidt penge = a little money / not much money
• lidt tid = a little time

No. They are related in idea, but they do different jobs.

• lidt = a little / a small amount
• lille = small / little

In this sentence, lidt is correct because it talks about quantity.

Examples:

• Vi har lidt tid. = We have a little time.
• Vi har et lille problem. = We have a small problem.

So use lidt for amount, and lille as an adjective describing a noun.

Because tid is being used in a general, uncountable sense.

In Danish, as in English, you often do not use an article with uncountable nouns when talking about an amount:

• lidt tid = a little time
• meget arbejde = a lot of work
• nok penge = enough money

So lidt tid works as a complete phrase without en or et.

I dag means today.

It is very common in Danish to place time expressions like i dag toward the end of the sentence:

• Vi har kun lidt tid i dag.

This sounds natural and neutral.

You can sometimes move time expressions to the front for emphasis:

• I dag har vi kun lidt tid.

That still means the same thing, but now today is highlighted more strongly.

Yes, absolutely.

Both are correct:

• Vi har kun lidt tid i dag.
• I dag har vi kun lidt tid.

The difference is emphasis and word order.

When i dag comes first, Danish uses normal main-clause word order with the verb before the subject:

• I dag
  • har
    • vi ...

This is a very important Danish pattern: if something other than the subject comes first, the finite verb usually comes second.

This is because Danish is a verb-second language in main clauses.

That means the finite verb usually comes in the second position:

• Vi har kun lidt tid i dag.
  Here, Vi is first, so har is second.

• I dag har vi kun lidt tid.
  Here, I dag is first, so har must still be second, and vi comes after it.

This is one of the most important word-order rules in Danish.

A natural pronunciation in connected speech is often smoother and less careful than the spelling suggests.

A learner-friendly approximation is:

• vi har kun lidt ti' i dai

A few useful notes:

• Vi often sounds like vee.
• har may sound fairly light in normal speech.
• kun has a long vowel.
• lidt is tricky; the d is not pronounced like a clear English d.
• tid may sound softer at the end than English speakers expect.
• dag in i dag often sounds closer to dai than a fully pronounced dag.

The exact pronunciation depends on region and speaking style, but in everyday Danish, words are often reduced quite a bit.

It is neutral and completely natural in everyday Danish.

• not especially formal
• not slangy
• appropriate in speech and writing

You could use it in many situations:

• at work
• in class
• while making plans
• in everyday conversation

So it is a very useful standard sentence pattern to learn.