If an adjective is being modified by a deictic degree adverb such as so, too, as, this or that then the adjective and adverb must go before, not after, the indefinite article. They can also appear as a postmodifier after the noun:
There are several grammatical points about this construction. Firstly, note that the adjective precedes the article here. The adjective is modifying a whole noun phrase, not a nominal (a nominal is just the smaller phrase within a noun phrase that occurs after the determiners or articles). So we see:
Secondly you will have noticed that this adjective is itself modified by an adverb. Now this adverb must (a) be an adverb of degree and (b) must be a deictic word, in other words it is understood by reference to the immediate environment of the speaker, or through some other element of the discourse itself. Simply using a normal degree adverb will not work here:
- *He was very good a footballer as ...
- *He was extremely good a footballer that ...
The adverbs that can be used like this are so, too, as, this, that as well as how. Some grammarians have also included more, less and enough in this list, but the grammar of these adverbs is in fact significantly different. Notice that this and that are adverbs here, not determiners.
The adverbs so, too, as, how, this, that and how are degree adverbs that cannot themselves give us any idea of actual degree or extent involved. We could think of them as a kind of 'pro - degree adverb'. These adverbs require some kind of benchmark for us to appreciate the actual degree involved. If this information is not provided by the context this normally entails there being a Complement phrase which indicates the actual extent or degree involved. We can consider such sentences in this way:
- It was (X)big a problem [that we gave up the whole project]
Here (X) represents the degree involved. On its own (X) does not tell us the actual degree of the bigness of the problem. It is the clause in brackets which explains the actual extent of the size of the problem.
The adverb involved will dictate what kind of phrase or clause can function as the Complement. The adverb so can take preposition phrases headed by the preposition as or finite clauses typically using the subordinator that. In the sentence above the only possible adverb we could use instead of (X) is the adverb so.
The adverb as typically takes phrases headed by as. It cannot take clauses headed by that.
The adverb too takes to-infinitival clauses, headed by for if they include a Subject:
- He was so big an idiot [that he wasn't allowed to speak in public without his advisors].
- It was so forceful a blow [as to fell his opponent].
- He is as great an actor [as has ever graced this stage].
- He is as good a footballer [as the next]'
- He was too valuable an asset [to let go].
- It was too dangerous a project [for us to take it on].
The preposition as (as opposed to the degree adverb) introduces equality with what follows it. More precisely it indicates some kind of benchmark which is met or exceeded.
Notice that the deictic degree adverbs this, that and how usually don't require a following phrase to provide the benchmark. It is normally clear from the discourse itself. However that sometimes takes finite clauses with that to provide a benchmark when it isn't available from the discourse:
- It was that big [that I couldn't fit it through the door].
Lastly, when how is interrogative as opposed to exclamative then it is not deictic - in the sense that the degree expressed is left unresolved and in direct questions may be expected to be supplied by the respondent:
- I wondered how long a journey it actually was.
- How long a rope do we need?
Notice that we cannot generally put adjectives before articles, the following are badly formed:
- *big a footballer
- *clever an idea
This only occurs when the adjective is being modified by a deictic degree adverb. Why? I don't know. I've been looking into this for quite a long time but haven't been able to find out.
The Original Poster's Examples:
Sentences (1) and (2) are grammatical. Sentence (3) is also grammatical, but this is because the adjective big is not being modified by any adverb. The word that here is a Determiner. Sentence (4) is completely ungrammatical. Because day is singular we must use a Determiner here. If we used an indefinite article then because warm is being modified by a deictic degree adverb, the adverb adjective combination should precede the article - as in sentence (2).
Note: Thanks to Edwin and fdb for helpful observations, which have been edited into the answer.