Apropos of a recent conversation in the comments, it’s worth noting that Americans generally pronounce /t/ in words like “button” and “Manhattan” in a different manner than one might expect.
To take one contrasting example, Americans pronounce the word “butter” with an alveolar tap (bʌɾɹ̩ or “budder”), while folks like myself pronounce the /t/ in “button” with a glottal stop (bʌʔn̩ or “buh’n”). In other words, American speech exhibits an exception when it comes to /t/ when it occurs before a syllabic /n/.
In fact, I’d say the glottal stop (or at the very least glottal release–bʌtʔn̩) is the unmarked American pronunciation for such words [Ed-and/or via a nasal release; see comments]. Why is this? As with a lot of situations of exceptional pronunciations, ease of articulation is partially the culprit.
In the case of the glottal stop, we start with something of a glottal-reinforced /t/. Because /t/ and /n/ involve the tongue being in the same position (the alveolar ridge), the only way we really know there is a /t/ is the sound of the glottis quickly closing then opening in a transition from /ʌ/ to /t/ to /n/. This ends up rendering the /t/ itself somewhat redundant, so many Americans simply hold off on moving their tongue into position until it’s time to make the /n/ sound.*
If you didn’t follow that unwiedly description, don’t worry; it’s besides the point. The more pertinent question is why we don’t use the alveolar tap here; that is, why don’t Americans pronounce “button” as “buddin?”
In fact, it seems to me that some accents that use the alveolar tap for /t/ actually do use it in “button” as well. I once had an Australian coworker from Brisbane who very clearly pronounced this word “buddin’.” (Although I should preface this observation once again by say that given the relative rarity of “button” in speech, I would need to hear many more Australians say it to come any conclusions.) It’s not entirely clear to me why many Americans have not gone this same route.
What’s also interesting here is that it suggests the neutralization of /t/ and /d/ in between vowels (or before syllabic consonants) is not entirely complete. That is to say, we Americans still do make some kind of distinction between /t/ and /d/, even if it’s mostly just in our heads.
*This is really a fairly common thing in English (and other languages). Similarly, we often drop the actual /n/ in the word “went,” leaving only a nasal consonant (wɛ̃t); and people will often drop the actual coronal movement in words like “belt,” leaving only a velar approximant (bɛɰt), even those who don’t normally have l-vocalization as a feature of their accent.