Some states deny extensions for underpayment of tax, but the IRS does not. There is no provision in federal tax law that denies the extension for lack of payment. However, late payment penalties accrue immediately along with interest.
While you're required to "properly estimate" you're not required to pay (it even says this on the form instructions, though those aren't binding law.) The IRS will not deny your extension so long as it is filed on time.
