A pocket veto is not available, as you point out, Congress will be in session when the clock expires.
rwfromkansas says in 231 that the bill has a provision that says it becomes law in 10 days if the President does not veto it. (Seems like usurpation of executive powers to me)
That provision, then, is de facto unconstitutional, as is the section that says you can find one part unconstitutional, but not others.