Theoretically, no hay problema; they will stamp your entry permit and your passport, and put the entry document in your passport (do not lose it; you will be asked to give it up on departure.)

But also theoretically - if your departure becomes delayed for any reason, of you deal with someone with little power and a big authority problem, you could technically get hassled; not likely, but... If it were me, I'd get the passports renewed before going - give the US Passport Office plenty of time, because there will likely be a rush with the new deadlines for passport required travel approaching.