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.