So orenr looked up the actual rhythm in the sheet music and explained it to me in a comment. And I guess I can see how it fits the structure, but I have a lot of trouble making it match what my ear hears. So in the tradition of that post I wrote some time ago about a Janet Jackson song, here's a breakdown.
The actual notes of the vocal melody fall in the following pattern:
The | marks the first beat of the next section. Not reflected in the above is other information that is relevant to determining the measure and beats, like melodies, chord changes, percussion instruments.
Anyway, it breaks down fairly unambiguously:
1...2...3...4... #.##......#.#... #.##......#.#... #.##......#.#. #.##......#.#...#.#...#.#.
Now remember that your basic rock/pop drum style to accompany this (although it's not done this way in the break) would be:
1...2...3...4... b...s...b...s... b = bass drum, s = snare
Comparing these, we see that the second half of each vocal phrase, the second syllable falls on 4, one of the snare drum "backbeats" (sort of resolving the tension of the first phrase stopping on a strong syncopation just before the first backbeat); and it in fact the second is the accented syllable of each: "there's hope" "a gift" "come true" "you work" ("so hard" and "all day" are two "extra" phrases), and then "life sends" "and friends" "and bends" "it ends" (and "well that" "depends"). The only thing is that it's not accented melodically (both syllables get the same note), and the delivery doesn't really stress the syllables in any other way--it's just in how they fall on the beat (and the fact that they rhyme, for those that do). Note in particular that of the "extra" phrases, only 'depends' is really unambiguously stressed on the second syllable out of this context (and is the only one that rhymes).
Even the third line is fine with this interpretation; there's a long-standing tradition of 7/8 having four strong beats, but simply ending an eighth note early compared to 4/4. There's another tradition where there are only three strong beats, e.g. Rush's Subdivision; but e.g. most of Jesus Christ Superstar's 7/8 is four beats, e.g. Anthony Stewart Head's brother sang "NAZarETH your FAMous SON / SHOULD have STAYED a GREAT unKNOWN / LIKE his FATHer CARVing WOOD / HE'D have MADE goo-OOD".
So now let's take a look at how I hear the breakdown of the final clause, and the official notation:
1...2...3...4... 1...2...3...4... 4/4 O.oO......o.O... 4/4 O.oO......o.O... 4/4 O.oO......o.O... 4/4 O.oO......o.O... 7/8 O.oO......o.O. 7/8 O.oO......o.O. 4/4 O.oO......o.O... 7/8 O.oO......o.O. 220.127.116.11.5. 1.x.x.2.x.x. 5/8 o.O...o.O. 6/8 ..o.O...o.O.
Here I've indicated stressed syllables as capitalized. However, the final line, where the stresses go is not entirely obvious, since as I noted only one of them actually has a rhyme or a natural stress. However, the melodic resemblence to the other line-ending bits makes it fairly unambiguous (if not audible) that they're meant to be the same, that is, iambs. So that's how I've notated them.
A few things are obvious on the official version, on the right. It stresses how the third and fourth lines are identical (whereas my version doesn't make it so), and it makes the two extra phrases more or less identical to each other.
But one thing called out by both versions is that the stressed syllables don't actually fall in naturally stressed positions. The 6/8 version is particularly awkward because it pushes them away from both beats. The 5/8 version is odd because it puts the presumably unstressed syllables onto the most likely beats (1 and most likely 4).
However, there is a drum sound on the 1 & 2 of the 6/8 version. The same sound falls in the 3 of the 7/8. In fact, what's entirely missing from either of the above is that the extra phrases are basically identical to the capping phrases from the previous lines. Here's something to try to notate that:
18.104.22.168. (counting eighth notes) 2/4 #.##.... Where there's life 2/4 ..#.#... There's hope 2/4 #.##.... Every day's 2/4 ..#.#... a gift 2/4 #.##.... Wishes can 3/8 ..#.#. come true 2/4 #.##.... Whistle while 3/8 ..#.#. you work 3/8 ..#.#. so hard 3/8 ..#.#. all day
I think this stresses what's really going on. And if you take that and recombine phrases, you'll get back the official score version of it. But that simply calling those last two phrases 6/8 is misleading about their relation to the previous measure, and where the accents naturally are, since in the earlier 3/8ths the emphasis is on 1 & 3 (counting eighth notes). Although I think this wonkiness of the accents actually causes those lines to sound less metrically iambic and more spondee, and also accounts for part of why I found the song disorienting to work out even when I counted it.
In fact, it looks like the official score gets this wrong in a subtle way. Here's a bit from the score that Oren just posted in another comment while I was writing this. While it is visually very clear the parallel between the 6/8 measure and the last half of the previous 7/8 measure, if you think about it, the 7/8 measure is, I think, notated wrongly. In music notation, we link together the notes from each quarter note, so, for example, the first three notes of each measure are all connected. The last two notes of each 4/4 measure are not connected, because that connection would cross a quarter-note boundary. This provides a way of seeing at a glance where the beats fall, emphasizing that it's the second note of each of those pairs that falls on a beat, as I mentioned before.
But now look at the 7/8 variation--here the last two eighth notes have been linked, as if the metrical accent is on the first eighth note, not the second. I don't think that's how it should be written at all, unless you really want to move the accent onto the first note. And this is the obvious visual parallel that you can see in the 6/8 measure, but there the same complaint still applies.
(Holy cow that's a wonky chord. Gm9 with a #5th over it.)
So, the big finish: it's pretty wonky, and just notating measure lengths doesn't really explain the audible effect very well, due to a (IMO poor) interaction between rhymthic emphasis and written emphasis.