A huge and perennial problem. The most pressing need by far is more runways at the major airports. Terminal expansions can generally get passed, but runway capacity expansions generally get stopped cold by NIMBY and environmental groups. Chicago O'Hare, Boston-Logan, and San-Francisco SFO all have land available on property, or can build into bays, quite easily from a physical perspective. But the US political system that allows localities to tie up nationally-important projects virtually without check, prevents such improvements from happening.
Second, even terminal capacity is strained at many airports, notably Los Angeles LAX and Boston-Logan. Both of these airports' terminals are tightly locked by runway patterns and are difficult to expand. New airports
Third, road connections from many major airports to downtowns are congested, and most major US airports don't have good rail links to downtowns. Mainline subway systems make many stops and are poorly suited for handling travelers with luggage; they work well at downtown airports where most of the traffic is in-and-out business travel (eg Washington DCA).
Most major US airports could use high-speed rail to downtown areas, but such systems cost more than most localities want to pay. A projected high-speed, direct train for Washington Dulles--Downtown DC (27 miles) would cost several billion dollars. This is on top of two billion the airport is already about to spend on an Atlanta-style underground rail system between terminals.
Need a new airline paint scheme? Better call Saul! (Bass that is)