When you can't give them attention, you need to give an overdone and thorough explanation that makes it absolutely clear that you are not blowing them off in any way, and are not devaluing them, or "sticking" one to them at all.
Yea, this happened when I had a date on a night my best friend wanted to hang out. She was deeply offended that I was "choosing to hang out with my boyfriend over her" and I had to give an indepth explanation of my actions. Afterwards, she felt awful for putting me in such an impossible position (especially since we had not verbalized any plans with one another that night) but that wasn't until AFTER she made me feel like an awful friend. ENFPs, why in the world does something like this make you feel rejected? Do you normally set plans in your head with someone without verbalizing them, thus holding that person to a standard that they can never meet, and then feel rejected when they do not do what you wish they would do? I can see this a little in myself, so I guess it may be an NF thing - but I tend verbalize set plans much better & I don't take it personally if a friend hangs out with someone else when nothing was set in stone.