It isn't necessary to feel obliged to anyone. Especially the ones close to you.
If you say "I Can't" and they don't understand, they're not as close to you as you think.
I had promised that I'd do something for a close one, but later realised I just couldn't.
I couldn't bring myself to say it out aloud, and spent almost a day in anxiety.
Then came the inevitable - and I blurted the fact out.
The reaction was much different from what I had anticipated, and made me glad I was friends with someone that sensible.
A video I saw today on TV was talking about something similar: "Your life is like the flame of a candle; no one knows when it will go out. You have to do all you can to protect it from getting smothered. Switch the fan off, cover it with your hands, kick others out. Do whatever you have to, but don't let the flame get smothered."
From now on, I will try to say "I can't" every time I should. At least, I will save myself from some unwanted work. If you understand, thank you for respecting my choice; I am grateful. If you don't - Thank you for letting me know what to expect from you.