If you're not able to submit and file your tax return and tax owed by the deadline, you should at least file for an extension by that date.
If you were expecting a refund, being late on submitting your forms isn't a big deal - there is no penalty for failing to file your federal tax return by the deadline. However, this might not be the case for state taxes.
But if you end up owing a payment, the IRS will charge late fees every month - so don't delay.
If you file an extension, you are exempt from late fees - but that doesn’t mean an extension on the time to pay your taxes. If you expect to owe money, you're required to estimate the amount due, and pay it with your Form 4868. As long as you do that, the extension will be granted automatically.
Of course, it's never too late to pay money you owe to the IRS. If you failed to file or to pay what you owed in past years, you can file a "back tax return" now.
One way or the other, there are compelling reasons to get on with it and file your return.