Snopes does not list this as "false," so you might want to check it out with the IRS or your local congressman.
Income taxes are normally due on April 15th unless that date falls on a Saturday or Sunday, in which case they are due on Monday the 16th or 17th.
However, there's a new timeline being follwed this year. Tax payments will not be due until you are nominated to a U.S. Cabinet position.
Please check with your tax adviser to confirm.