If you have e-filed your original return and had tax due, you should have gotten a 1040-V with your tax return to mail in with a check (unless you did a direct debit from your checking account).
This check must be mailed by April 18, 2017, or else it is considered a late payment.
It's very unlikely that your amendment would be processed by then, even if you mailed it today.
Since the e-file process and the amendment process are totally separate down at the IRS, they don't have a way to net a refund against a tax due.
So go ahead and make your payment on the original return (unless, as I noted, you did a direct debit), and then file your amended return, and your refund will come eventually.