Oh my goodness you must be a wreck but hang in there.
First of all, consider that there may have been a typo or problem in the RSVP information.
In any event, you should definitely get on the phone and call the parents. Tell them that you were concerned that there was a typo on the invite, that the envelope was small or a weird shape and got lost in the mail, that you put the wrong postage on, that you got some but not all of them back from the PO today with mangled corners, any little white lie that gets them off the hook gracefully for not having responded.
Tell them you are new to the school, the area, whatever, and that you were hoping for a chance to meet some other parents however briefly to find out how their experience has been at the school. If they still say they can't come, see if you can't right there and then schedule a one-on-one playdate for your daughter, perhaps with Mom along for the ride for a coffee...a walk in the park? A little gardening project? Make it sound fun and creative if you can.
Don't give up, think of this glitch as a little silver lining in your raincloud and try to make something good come of it, even if it's just a playdate or two.
If your daughter is painfully aware of her birthday party date and it looks like nobody or only 1-2 others are coming, change the plan and take them somewhere special, for a manicure, or out to lunch or to a movie (the new Dragon movie) so that it doesn't feel like an empty party, or if you can import some cousins on short notice, do that.
I really hope it's just the usual frantic sloppiness on the part of other parents that has caused this problem for you, and if not, that you can parlay this into a small success. Hang in there!
-- K.