It never hurts to ask at check-in! The best way to phrase it is to ask if there are any better rates available than the one you've already booked. Many staff will normally just say no, or will say that they can't change your rate (often true due to cancellation policies/etc) - but I've been successful at least a few times.
For the most part the best way to get discounts at hotels in the US is to try and get a "corporate" discount. These are prearranged discounts companies have with specific chains that will normally give a discounted price and/or special conditions (free breakfast, free parking, etc).
If you work for a large company you may find that they have such deals with at least one chain, and in many cases these discounts can be used for leisure travel as well as business travel. There are also a number of membership-based organizations that offer similar discounts, such as AAA, USAA, or even Costco! In theory you will need to show proof of membership at check-in, but in practice that rarely happens. Sometimes there will be a check-box on the booking website for these (especially for AAA). Otherwise you need to get a code from the organization, and/or book via their website (eg, Costco travel).
Otherwise you can try calling the hotel and seeing if they will offer a cheaper rate. In general the answer will be no unless there are special circumstances (eg, if you're booking more than about 4 rooms you can probably arrange a discount) - but it never hurts to ask! Make sure that you call the actual hotel themselves, and not their central reservations department who will not be able to offer you anything special.