I can't see why she can't do that. Essentially she hasn't officially resigned yet. She won't be officially resigned until they find a replacement for her:

"effective upon the nomination and confirmation of my successor."

Therefore she is still a Supreme Court Justice, and will legally remain so until a successor is found.

Yes but that effectively deprives the President of his Constitutional authority to make a recess appointment. To put the condition another way: "I will retire if you use option 1 rather than option 2, both of which you are otherwise free to use."

Odd.

I don't think it's odd in the sense of "unusual" though. Supreme Court Justices require conditionally quite regularly. I confess it is not clear to me how you can nominate somebody to a seat that has not been vacated, (and O'Connor's seat is not vacated until the nominee is confirmed, which he can't be until he's nominated . . . ) but that is the way it is done.

I know you all have your own pocket versions, but I couldn't help myself:

"He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments."

Nominate: propose as a candidate

Confirmation: Action by the Senate approving Presidential nominees for the executive branch, regulatory commissions, and certain other positions.

appoint: assign a duty, responsibility or obligation to

So, Bush will propose Janice Rogers Brown, and the Senate will approve her. With that approval, (and not a second before), Justice O'Connor is no longer a sitting Justice as per her contract with Bush. At that point, Bush can assign Janice Rogers Brown to take O'Connor's seat.

"The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session."

Bush can't make a recess appointment because there is no seat to fill. We all know Justice O'Connor is going out the door, but she'd still sit to hear a case if timliness was an issue. That means she could still sit to hear cases next term if nobody makes it through the requirements Justice O'Connor has laid out.

What vacancy? Justice O'Connor is still here!

I think we're looking at two sides of the same coin. I agree with everything you said. The question is whether the condition is an acceptable one under our separation of powers. And my point is precisely that, her letter deprives the President of the opportunity to make a recess appointment (for better or for worse).

Again, I'm not asking about what the condtion is, but its propriety.

What if Bush were to make a recess appointment and subsequently, when the Senate considers confirmation, the Senate does not confirm, would O'Connor under the terms of her conditional resignation then be able to resume serving as a Justice? Would she have contractual rights?

Query as to the origionalist view of O'Connor's conditional resignation? What was the original intent of the framers/founders, the original meaning of the recess appointment provision, the then public (whomever that may consist of) understanding of that provision? Let's discuss this further during recess while we all look for the lost Constitution.