As far as I know, the only GUARANTEED services are Express Mail, and Global Express Guaranteed. Mail sent using these services is supposed to arrive by a certain time. And you will pay extra for this.
All other classes of mail will be there when they get there. Though USPS says "your packages reach their destination in 2-3 days", they do not make a promise about that. And of course, Sundays do not count in that 2-3 day total.
In our experience, packages DO generally get delivered in 2-3 days (not counting Sundays), though weather can cause delays, and the few days before Christmas are also "dicey".