-Pay the full amount. If your taxes are too big for you to pay in full, first double-check your math. Make sure you've claimed every permissible deduction. If you're unsure whether something is deductable, ask the Taxpayer Advocate Service, whose advice is free. They can answer questions on a wide range of topics before you file, and, afterwards, can tell you the status of your tax refund. If you don't have enough cash to pay your taxes, pay by credit card though fees are involved.
-Can't pay it all? Pay some. The IRS looks favorably on filers they believe are making a good faith effort. While you have to make "a payment" to the IRS on or by the April 18, that payment can be as little as $1. Pay that minimum, and you won't have broken any rule--though you will have to pay interest to the IRS on what you owe, plus any penalties. If you owe $25,000 or less (in combined tax, penalties and interest), you can get permission to pay in installments by filing Form 9465 and using the Online Payment Agreement (OPA). Taxpayers with annual incomes of up to $100,000 and tax liabilities up to $50,000 can enter into an agreement with the IRS called an Offer in Compromise, which settles the taxpayer's tax liabilities for less than the full amount owed, subject to IRS approval, which is by no means a given.
Persons unable to pay their taxes because they are suffering or expect to suffer economic hardship can ask the Taxpayer Advocate Service to intervene on their behalf.