Does T become S sometimes in casual American speech?

Question

Taylor Swift is American and I was listening to her song named "You belong with me". You can hear the song on Taylor Swift's official YT channel.

In this song (from 0:48 to 0:52), she says:

That what you're looking for has been here the whole time (listen to it).

But she says the "time" as if it were "sam", the T is S.

The song with lyrics

I also checked some other sites for its lyrics but it is "time" which is being pronounced with an S.

Research:

I did not find anything but another question on this site.
Only the second answer seems to have explained it partially, I will quote it here:

I don't know for sure, but I'd guess that the [d] in fid'na comes from the [s] in fixing to, the way that the [z] in isn't, wasn't or business can turn into [d] in some accents before the following [n] sound. Something like [ˈfɪksɪntə] > [ˈfɪksnə] > [ˈfɪsnə] > [ˈfɪznə] > [ˈfɪdnə].

If the intermediate pronunciations [ˈfɪsnə] and [ˈfɪznə] exist, that would support my guess."

The answerer over there says [ˈfɪksɪntə] > [ˈfɪksnə] > [ˈfɪsnə] > [ˈfɪznə] > [ˈfɪdnə].

Question:

Do Americans sometimes pronounce the T as S?

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EDIT:

Also hear "A thousand years" sung by Christina Perri (American)

At 1:48, she says: "standing in front of me" but the T in the front sounds to me like an S.

Answer 1

To get simple things out of the way quickly, no, in current American speech there is no general trend towards changing word initial /t/ to /s/.

The sound that you hear in that song is probably literally a slip of the tongue or a peculiarity of that speaker for just that word. The singer does make a similar sound with the same word once later in the song, but doesn't do it with any other instances ('typical' and 'Tuesday' don't have the fricative onset that sounds like an 's'). That is, she doesn't seem to always change /t/ to ... that weird thing she does that's sort of like /st/ but maybe /t/ and /s/ at the same time.

Also, more to the point of the question in the title, it just isn't a pattern in Modern Standard American English or really any other variety of English (BrE, IrE, ScE, AusE, IndE, NigE, SiE, etc etc or any subdialects of any of those).... that I'm aware of.

However, this is not to deny the plausibility of such a direct sound change of /t/ to /s/. In ModE, word initial unvoiced plosives (p,t,k) are all aspirated, and /t/ is articulated in the same place as /s/ (dental or alveolar), and nearby articulations/perceptions often get changed into the other. Also, historically, the High German Consonant Shift led West Germanic (parent language of English, Dutch, and German) to change intervocalic t to s for example eat/eten/essen, water/water/wasser.

So there is a possibility that word initial /t/ in general -could- change to /s/, but there is no evidence that it is doing so in any variety of Modern English.

Answer 2

I see exactly what you mean. When she says "sime" it is a slip of the tongue. She is singing a bit "country" and people who speak "country" are considered to have a "drawl" but this to me sounds like a mistake. Just a slip of the tongue that was left in when it was mixed.