When you amend your return, you're starting out at zero. Anything you get back on your original return you'll get back. Anything you owe with your original return you'll owe.
The amended amount (whether you are getting an additional refund OR owe additional tax) is a separate transaction.
So in your case, you'll pay the original amount first, then owe on your amended.
You have till April 18 to pay the amount due with your amended return.