If so, do not be afraid to apply for one. As long as you make a good faith estimate of how much you owe and report your withholding and estimates accurately, then the extension is automatic. An extension is an extension of time to file your return not an extension of time to pay. IRS has more details on their website.
Most states, but not all, require you to file a separate extension form with them. You can get an IRS extension form 4868 from the IRS’ website – IRS.gov. At this time of year, form 4868 is one of the forms listed on IRS’ home page. A direct link is here (PDF). You need tax software, including the IRS Free File, to file the extension electronically. Please understand that the IRS Free File goes through commercial entities and there are limitations.
NC’s individual extension form is D-410. The link leads you to a page describing the process and allowing you to file and pay any tax due online.
If you are unable to pay but are otherwise done with your return then file and ask IRS and any states for a payment plan. Not filing the return and not filing an extension when you owe will result in much higher penalties than filing timely without the payment. Assuming you file on time and do not pay, there are still late payment penalties and interest. However, the late payment penalty with IRS is 0.5% per month of the amount unpaid on April 15th. On the other hand, the IRS late filing penalty is 5.0% (yes ten times larger) per month of the amount unpaid by the original deadline.
Contrary to urban rumor, an extension does not increase or decrease your chances of being audited.