I have just received a very helpful message from one of the attorneys working on an amicus curiae brief in support of the United States in Florida v. HHS. He has spoken with the clerk's office of the Eleventh Circuit in Atlanta, and clarified any ambiguity: amicus briefs in support of the United States are due MONDAY, APRIL 11 (and not this Friday). (To be specific, this is the day that the hard copies are due, according to this attorney.)
Apparently, the Department of Justice "tendered" its brief on Friday, but did not officially "file" its brief until yesterday, April 4. Thus, the seven-day clock for the filing of an amicus brief began to run yesterday, giving parties until Monday under Federal Rule of Appellate Procedure 29(e).
Sorry for the confusion.