Original Sin does not mean that God charges us Adam and Eve’s sin as if we had committed it.So what is the orthodox reformed position? Inasmuch as that is synonymous with what is found in the Reformed confessions I turn to the Westminster Confession which teaches:
VI.I. Our first parents, being seduced by the subtlety and temptations of Satan, sinned, in eating the forbidden fruit. This their sin, God was pleased, according to His wise and holy counsel, to permit, having purposed to order it to His own glory. 
VI.II. By this sin they fell from their original righteousness and communion, with God,  and so became dead in sin,  and wholly defiled in all the parts and faculties of soul and body. 
VI.III. They being the root of all mankind, the guilt of this sin was imputed;  and the same death in sin, and corrupted nature, conveyed to all their posterity descending from them by ordinary generation. 
(I wish I could write as cogently and economically as the Westminster divines.)
The points relevant for this discussion are  and . The Westminster Confession provides the following scriptural support:
 GEN 1:27 So God created man in his own image, in the image of God created he him; male and female created he them. 28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth. 2:10 And a river went out of Eden to water the garden; and from thence it was parted, and became into four heads. 17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
ACT 17:26 And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation.
ROM 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned. 15 But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. 16 And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification. 17 For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.) 18 Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life. 19 For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.
1CO 15:21 For since by man came death, by man came also the resurrection of the dead. 22 For as in Adam all die, even so in Christ shall all be made alive. 45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit. 49 And as we have borne the image of the earthy, we shall also bear the image of the heavenly.
 PSA 51:5 Behold, I was shapen in iniquity; and in sin did my mother conceive me.
GEN 5:3 And Adam lived an hundred and thirty years, and begat a son in his own likeness, after his image; and called his name Seth.
JOB 14:4 Who can bring a clean thing out of an unclean? not one. 15:14 What is man, that he should be clean? and he which is born of a woman, that he should be righteous?
I am not convinced, in reading the scripture (some of which does no seem to apply), that Adam’s original sin of disobedience goes on our debit column along with all the multitudes of sins we will commit. Nor I am not convinced (although I feel less strongly about this point) that this Westminster Confession is teaching. I do know it is what many claim as the orthodox Reformed position.
No, as I wrote yesterday, the legacy of Adam’s sin is something much worse—a total corruption of man’s character that puts us in a state where we are unable not to sin. Total Depravity is our heritage; that is what the scripture above is teaching us.
My position is probably more accurately represented by stating that guilt for Adam’s sin of disobedience in insignificant in comparison to our own inevitable sins resulting from our being conceived and born in a fallen state. So I would argue that it is utterly Calvinistic to see this esoteric point as being unimportant.
I think the reason alarms go off is that it appears to open the door to the Pelagian heresy, which held that man is essentially good and has the ability to keep the law. Pelagius had to remove the concept of original sin to avoid the possibility of man living a perfect life (which he thought was possible) only to stand condemned by Adam’s sin.
Catholics are not Pelagian, but they have a similar concern with the precise nature of Original Sin because of their doctrine of Immaculate Conception.
The Reformed Position on Total Depravity means that this point is totally irrelevant. We stand condemned from the time of conception (Psalm 51:5) because of the effect of Adam’s sin, not the sin itself. We are awash in our own sins of commission and omission.
In a weird sense I agree with Pelagius that God does not have an ace-in-the-hole that he will pull out if someone leads a perfect life. We had a Covenant of Works before the Covenant of Grace, and it is still in effect. I believe that if someone did live a sinless life that God would honor that covenant and not say “Great job—but unfortunately there is still Adam’s disobedience which I charge against you.”
Unlike Pelagius I do not believe this gives us a chance to work our way to heaven-- again, the Total Depravity thing. There is no Pelagian window because it is not just hard but utterly impossible for anyone to live a sinless life. Once again from the Westminster Confession:
VII.II. The first covenant made with man was a covenant of works, wherein life was promised to Adam; and in him to his posterity, upon condition of perfect and personal obedience.
VII.III. Man, by his fall, having made himself incapable of life by that covenant, the Lord was pleased to make a second, commonly called the covenant of grace; wherein He freely offers unto sinners life and salvation by Jesus Christ; requiring of them faith in Him, that they may be saved, and promising to give unto all those that are ordained unto eternal life His Holy Spirit, to make them willing, and able to believe.