So cute!! And boy are they packed in there!
Carol's on the right track. If you can't identify the parents, try identifying their behavior. What time were you there? That might also help to narrow it down, what times they prefer to feed.
I love seeing these little guys hatching and watching them grow. I have no idea what type of bird they are and agree that watching for mom and dad would be the fastest way to find out. I also don't know much about low nesting birds. The robins tend to make their nests a bit higher around here.