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Likewise, [St Augustine] notes that death reigned even over those "who had not yet sinned of their own individual will, as Adam did, but had drawn from him original sin...because in him [Adam] was constituted the form of condemnation to his future progeny'' (Ibid. I.13; Fathers of the Church).

St Thomas writes that, "Wherefore, original justice being forfeited through the sin of our first parent; as human nature was stricken in the soul...also it became subject to corruption'' (Ibid. IaIIae.85.5; New Advent).  Through removal of original justice, "the sin our our first parent is the cause of death and all such like defects in human nature'' (Ibid.; New Advent). 

St Thomas continues, distinguishing between Adam's willful 1st sin and the effects of Original Sin of the rest of the human race, who are not guilty of Original Sin through their bad will but through nature.  ...Though original sin is a sin of the will of Adam, it is not a sin of his descendants "except inasmuch as this person [his descendant] receives his nature from his first parent, for which reason it is called the `sin of nature'' (Summa Theologica IaIIae.81.1; New Advent

First parent = Adam

Is not Christ, then, subject to Original Sin because He is an offspring of Adam?

Thomas Aquinas, on the other hand, finds that Jesus Christ, by virtue of his conception, would not be subject to original sin. Aquinas found that original sin passed to men since they were "one body'' with Adam (Summa Theologica IaIIae.81.1; New Advent). But Christ was not part of this body. As Aquinas notes, original sin is only contracted by those "who are descended from him [Adam] through seminal power'' (Ibid. IaIIae81.4; New Advent).

In other words, only those properly of the seed of Adam would be subject of original sin. Thus Aquinas concludes that ,''If anyone were to be formed by God out of human flesh, it is evident that the active power would not be derived from Adam. Consequently, he would not contract original sin'' (Ibid.; New Advent). Thus, Aquinas finds that Jesus Christ would have no need to cleanse his body of original sin, since his conception, by its independence from carnal generation, would have been without sin.

http://www.memoryhole.net/~chris/research/original_sin.html

Thomas Aquinas, on the other hand, finds that Jesus Christ, by virtue of his conception, would not be subject to original sin. Aquinas found that original sin passed to men since they were "one body'' with Adam (Summa Theologica IaIIae.81.1; New Advent). But Christ was not part of this body. As Aquinas notes, original sin is only contracted by those "who are descended from him [Adam] through seminal power'' (Ibid. IaIIae81.4; New Advent).

Interestingly, this makes it sound almost as if Original Sin is transmitted genetically.  So that's another question.  Is it transmitted physically or spiritually ... or through some combination of the two?

I once heard it said that Adam committed the first sin in falling asleep at the switch so to speak -- in negligently letting the snake get into the Garden in the first place!

I see what you're saying but I disagree.  St Augustine says that both Adam and Eve committed Original Sin before eating the apple because sin is committed first in the will.  He said that their desire for knowledge was a sin against pride first, then they sinned in action as a result of the loss of grace.

Since Eve sinned through her will and desire for knowledge, which are internal sins, it could be argued that such a sin could've taken place with or without the presence of the serpent.  So even if Adam had protected the garden from all external forces, the temptation to pride (which is the sin of the angels and arguably, the ONLY sin that Adam and Eve were capable of, since their reason, intellect and human nature had no disorders) would've always been an internal struggle.  In other words, God would've tested them in some other way, since Adam/Eve had to be tested just as the angels were.