Something I'd missed in the narration, that scene takes place on September 12th. Cap saying he slept yesterday means he slept before the planes hit. If it had been tomorrow, he would've said he slept two days ago. That line has always given me chills because of what it says about him, that there's no time to rest while there's work to do.
With most of the MU centered in NYC, all of them would've been hit pretty hard by it. Though Fury's may have reacted to it differently from Cap in this book, he at least understands the guy well enough to not be sore when Cap forcefully rejects the mission he tries to send him on.