Is there any combination of aircraft and airports where no alternate landing airport would be possible?
For larger aircraft, likely no. Worst case they can carry enough fuel to return to their origin. If range does became an issue (e.g. Atlanta -> Anchorage) you would just schedule a technical stop somewhere like Yellowknife. Alaska has a ton of small airfields so short-range aircraft would have many alternatives. Wether the alternate has any services is another question.

As the question asks about US airports only, mainland -> Hawaii would be a possibility. Hawaiian Air's 717 planes already need extra tanks in the fuselage to get to the mainland, so a return flight would be weather-dependent. If you take off from Seattle and several airports close for bad weather after you pass the no-return point your options are rather limited. If the weather is bad enough to close every airport in the islands then channeling Sullenberger won't help much. Unlikely any sane pilot would take off with that kind of forecast, and Hawaii's weather is usually pretty good.