I've not followed the comics, so I don't know who's "meant" to say it. But I'd assume it's going to be used in a far less cliche way that it sounds, and its going to be Fury saying "Assemble the Avengers" or something.
I suppose, with the interaction between Cap and Iron Man seen in the trailer, Cap might get all "Avengers Assemble!", everyone looks at him weird, and Iron Man makes some cutting remark.
Edit : Not just that, but watching the trailer again, every important soundbite is from Iron Man/Stark.. because Downey Jnr is the biggest name, bar Jackson, in that movie. I highly doubt they would not have either used it already if it was going to be said, or if it is going to be said that they will give it to anyone other than the character that the public view as the "leader" of the group.