If you know when your rent is due, why wait for the invoice? Drop your rent off on or before the due date, or mail it in plenty of time to arrive by the last acceptable day (keeping in mind holidays, etc. which may effect mail delivery). This will keep you out of the late fee hot water.
The date the check was postmarked makes no difference. The only thing that matters is that the check was in his or her hand by the due date. Usually, rent is due on the first of the month and you have until the fifth before it's late.
I would have to use the following example to answer your question. If I can recall right, the only collection agency which regards postage dates as relevant is the IRS. Most other places do not consider the mailing date of your bill as counting as received. Technically, if the check was not in their possession on the due date then it is considered late.
Basically, "the check is in the mail" simply does not work any more.
The most important thing in such cases is to make sure that you are very aware of your contract and what you have signed. Read all the smallprint! Refering to your contract should answer this question for you. Also, you might want to consider ringing them up if you remain unclear. It is important to not be late on a rent payment if you can at all help it, as that could have damaging consequences in the future.
In most cases (though landlord/tenant law is pretty varied around the country) rent is counted as received when the check arrives, so when you mail the check isn't as important as when it arrives at the landlord's. Still, two days should be plenty of time for the check to arrive by the due date.
You should check your rental contract (usually signed when you move in) and see what the terms are for their charging you late fees. If it's not in the contract you signed, they can't charge you. You might also consider hand delivering the payment if possible.