"Thank you so much and I'm very excited about this offer, but, as I'm sure you'll understand, I need a couple of days to discuss such a big move with my (significant other, pet llama, psychic grandmother, weird friends) before I can give you a definite answer. I will know for certain by one week from today."

I don't think you can string them along any longer than a week and even that much is risky.

Does the offer contain a time-frame for response? If it does (and I assume it does) then I'm not sure there's really a tactful way of saying "I'll get back to you on that." About the best you can do would be giving a hard deadline, i.e. "I will be sure to let you know my decision by X at Y PM", by which time you would have presumably figured out the details of the other job. Really all I'm trying to say is just be direct, give a definite time by which you'll have a verdict, not "I'll let you know". If the offer already includes a deadline, then you're really just negotiating to extend it.

But I'm really pretty clueless on these things so take this with a large grain of salt.

(psst, I'll tell you the way I did it. I don't reccomend this. I just avoided their calls and emails until I knew, then told them. Again, I DON'T RECCOMEND THIS).

Thanks guys! I managed muddgirl's strategy for a day or so, because I was out sick to begin with. Then I got a mystery number on my cell, answered it and said pretty much what mygothlaundry proposed, except pretty much told the truth about the other opportunity, because I don't think that will be a dealbreaker. I'm the only applicant to either position so far, so it should be all good.