Yes and no. There are no postmark checkers at the IRS. If you mail your return a few days late no one will notice. That being said, even if they did check for postage marks here's what the IRS can charge you.
Late penalty = 4.5% a month (up to 5 months), accrued daily.
Late interest = 0.5% per month plus IRS interest rate (Fed short term plus 3%, currently about 5% per annum = 11%/annum) accrued daily.
Late penalties works out to 0.15% per day.
Late interest works out to 0.03055% per day.
If you owe file late your daily I+P = $1.80 per day on every $1000. Weeeeeeeeee!
If you owe and file on time, there is no penalty, but they'll charge you the ~11%, or 0.03055% per day or 30 cents per day on every $1000. Weeeeee!
http://www.irs.gov/taxtopics/tc653.html
http://evans-legal.com/dan/afr.html