I'm assuming this is your manager making the threat and there is a separate HR department. If so then go to HR with your concern and only provide the HR person as your reference (which you should do anyways).
If not then I'd ask your new job if you can start sooner and explain the situation. You don't NEED to work a 2 week notice, it's nice that you are willing to do so but if they are not going to be happy with just a 2 week notice then give them nothing. I'd certainly not ask the new job to delay your start date, your obligation is to them now