With some speakers the articulation there can sound closer to [d] than to [t].
Pardy on, dude. Pardy on.
It depends where on the roof of the mouth the tongue makes contact. The farther back, the more the sounds shades towards [d].
The vowel in the first syllable, colored by [r], can be rather farther back in the throat than the counterpart in BrE, which is a more open vowel; that [r] can result in the cheeks tensing and the chin being pulled back as well, so that for some speakers of AmE there's quite a distance for the tongue to travel, indeed for the entire lower jaw to travel, to produce [t] and less distance for it to travel to produce [d].
An AmE speaker who retracts the lower jaw to produce [par] is almost guaranteed to articulate the consonant as [d].
But the direction of movement of the tongue to make the d/t is never front-to-back.