How to word this - backing away from a friendship

[Amara]

How about something like "I'm sorry. We'd just rather not." Too harsh?

[Danika]

It seems harsh to me. It would really hurt my feelings if I read that because it's a rejection. But I also agree with the posters who don't think I should string her along. I think a regular person might catch the subtlety of "let's not make plans right now." I don't think she will. But I feel like I should try that avenue first before I do too much, overcompensate and seem like I'm beating her off. I haven't sent a reply to her yet. I'll wait a day and see if anyone here has any other suggestions for me to consider. I appreciate all of the input I've received so far.

[TootsNYC]

I think if you try the "I really shouldn't make any plans right now" and being busy and not responding to her whiny emails, etc., and if that doesn't make her taper off, then you can say, "I'm discovering that I'm having trouble keeping up with my current social and family obligations, and I'm not in a position to take on a new close friendship."

Then it's one of those, "It's not you, it's me/my life" responses.

[Lynn2000]

I like TootsNYC's approach.

As a side note, one thing I've found helpful is to encourage the person I'm backing away from to find other people to do stuff with/do stuff without me. Like if she were to say, "Hey, I'm really looking forward to New Movie and I think you would like it too. Do you want to go with me?" I could reply, "Oh, I do want to see it, but I just don't know when I'll be able to fit it in. You go ahead and see it, though, don't wait for me." Or about attending a festival together, "I just don't think I'll be able to, but I hope you find someone else to go with, it sounds like you would really enjoy it."

It just seems a lot more positive to me than saying, "No, I don't want to" or "No, I don't have time." It conveys that you wish them well and has that "it's not you/it's me" vibe--"I can't, but I'm sure someone else out there would love to, because it's not an inherently bad idea." Plus, it explicitly avoids the whole "but I've been waiting until you could go with me!" guilt trip attempt. 

[Danika]

TootsNYC and Lynn2000, fantastic! I will do as you both just suggested. Thanks!