It's too late to apologize....

Something happened with a friend of mine last week...and the situation is eating at me. Makes me think of the song by Timbaland "Apologize". Not that the meaning of the song has anything to do with this situation...but still..the chorus says "It's too late to apologize" and that's how I feel about this. Since I canNOT seem to get it out of my mind, I thought I'd tell ya'll about it and see what you think. Of course, I am leaving out the specific details to protect identity...but you'll get the point I think.
So, I made a committment a couple of weeks ago to her to do something for her this past week. At first, I had said no because I knew it was going to be a busy week--with it being my birthday and having company come into town---but I knew she really needed help with this project and so I said I would do my best to help her out. (besides, she has ALWAYS helped me out when I needed it and so it was my turn to return the favor, I felt.) The day finally came and just as I thought, I was dreading it because I really just didn't have the time. We communicated with each other through several e-mails and everytime the mood was very relaxed and she was like "just whenever you can get it done will be fine." Well, long story short, after 3 days of trying to get it completed, I ended up telling her that I was almost done with it, but not quite and didn't know if she wanted to finish it up or if she wanted me to. That's when I realized that the mood about this was NOT relaxed as I had thought. The next string of e-mails were short and cut and dry (very NOT like her) and I knew she was MAD. I apologized over and over to the point of looking like an idiot begging for forgiveness. She ignored my offers to complete the task and my plea's for forgiveness and I haven't heard from her since. Because of the relationship that we have, we HAVE to see and talk to one another eventually...but I can't STAND this tension. I know I messed up. I admit that I should have given this committment top priority and gotten it done. I feel as though I dirtied my "name" and didn't keep my word and that feels awful. But what else can I do but tell her how sorry I am and offer to make it right?
I honestly don't think she has a right to be MAD at me. She might be frustrated that she had to finish up the last few minutes of something that I was supposed to have done for her...but I can't believe it is this big of a deal to her that she would downright ignore me and shut me out. I think I've probably done all that I could do at this point...but still, I find myself thinking about this and worrying about it non-stop. I guess it's just that nature inside of me that wants everyone to like me. I can't stand to think I've hurt someones feelings or not come through for them. That goes against everything that matters to me--everything I stand for. Yet, now--after the fact, what can I do?
Anyone have any suggestions?
Should I just try to forget about it? Should I say sorry again? Should I send her a card in the mail just reiterating how sorry I am? Should I just be short and cut-n-dry with her right back?
BTW..I HAVE prayed about it and asked God to soften her heart towards me and forgive me.