1) Pronunciation in songs doesn't "count." I'll explain that in a minute. 2) As a U.S. native speaker, I don't really think of "t'day" and "tooday" as different pronunciations. I think of them as just being typical of the way pronunciations get modified depending on how fast or how slow, how carefully or how casually you are speaking. In my mind, I "think" the same phonemes, but when I speak them they come out as "t'day" usually, or "tooday" if there's some reason I'm speaking slowly, carefully, or trying to emphasize that word. Pronunciations always get modified in smooth, flowing, continuous speech. That's why learners have trouble with natural, colloquial, rapid speech. By the way, both oxforddictionaries.com (U.K.) and ahdictionary.com (U.S.) list only one pronunciation: /təˈdeɪ/ , "t'day." 3) You might say "tooday" if you are being dramatic, speaking to a crowd, and want to make it clear that you are making a contrast. "And when, my friends, when does this happen? Not yesterday, not tomorrow, but... TOODAY." To get back to "songs don't count:" in songs, pronunciations are often modified to fit the tune or the rhythm, and are often strung out. Furthermore, English isn't a very good language for singing because we have some twenty-odd vowels, and most of them are not the nice clear open "ringing" vowels that sing well. Italian, for example, is much better. Furthermore, vowels sing well and consonants do not. Virtually all singing teachers actually teach singers to modify the pronunciations of words, usually by stretching out the vowels and shortening the consonants. It is natural to sing "tooday" to give the pitch of the note a chance to be heard. So, enjoy songs but don't take them as a reliable guide to the pronunciation of spoken English.

American here. In normal speech, we too, say "t'day" or "tuh-day". However, when we are really enunciating and slowing our rate of speech down, we are more likely to say "to-day". Since this is a kid's song they're speaking much more slowly and clearly than someone normally would.

it depends on how you want to say it. If you say it clear and slow it should be : "2 DAY" with the emphasis on "day" We often speak it quickly so it comes out sounding like "tday" with the "o" sound omitted again with the emphasis on "day" At medium speed , it might sound like "ti day" with the "i" sounding like the "i" in "sit" with the emphasis on "day" Take your pick , but I suggest the first one.

In England, we say "t'day" - in other words, we do not say "toooooo-day".

Got it. Thanks for your answers. :-)