These words are not pronounced with d in American. They are pronounced with an alveolar flap. In general American, this consonant replaces both t and d when they lie between two vowels, the first of which is stressed, and it sounds very much like a d to British ears.
If you pronounce these words with a regular t, Americans will understand you perfectly, although it will contribute to an impression of a foreign accent (my guess is that it would sound like a very slight Spanish accent if you pronounce everything but these t's and d's the way Americans do). If you pronounce these words with a regular d, I believe Americans would be more likely to misunderstand you, although I don't know whether anybody has studied it.