Many linguists argue that the underlying past tense allomorph is /d/. They base this argument on the claim that it has the widest distribution. However, though it occurs after alveolar plosives, i.e., "wanted" and "needed", and voiced consonants, i.e., "healed", is it not necessarily unconditioned after an alveolar plosive and vowel. One could argue that the plosive is voiced because it follows a voiced vowel.
There is another clear fallacy in the argument. The statement that we should choose /d/ because it has the widest distribution contradicts the notion that an alloform should be contextually determined. The number of alloforms is equivalent to the number of contexts in which they occur. In this sense, no alloform has a wider distribution than any other. Unfortunately, many linguistic analyses involve the principle that if it works, it is fine.
The notion of an underlying form seems to imply that the alloforms were derived from an abstract form. However, the possibility remains that all variations were derived simultaneously in a specific context. This can occur as a result of linguistic variation.
However, if we must choose an underlying form of the English past tense marker, it makes sense to choose /Id/. Historical evidence can be given to support this allomorph. In the movie King Henry V, Kenneth Branagh pronounces past tense verbs such as "remembered" with /Id/. Ancient texts often show spellings such as "remember'd" to indicate that a vowel which is usually pronounced has been deleted.
The Danish language, a related Germanic language, has past tense verbs such as "huskede" (remembered) and "elskede" (loved) in which the vowels are never deleted. Norwegian has "husket" and "elsket" for these respective verbs. We can also argue that if /Id/ is underlying, we apply deletion to derive the other forms. Deletion appears to be more common that insertion with respect to phonological processes.
How do we derive the other past tense allomorphs if /Id/ is underlying? The verb "wanted" requires no phonological process. It is simply want + /Id/. The verb "asked" is "ask" + /Id/. Deletion gives us "ask" + /d/. We then apply a voicing assimilation to make the alveolar plosive voiceless. The verb "spilled" is "spill" + /Id/. Deletion gives us "spill" + /d/. To me this seems more plausible and elegant than choosing /d/ as underlying.