I'm working on a mod that revolves around the presidency at the time of the war with China and/or the bombing of Washington. Is it documented anywhere who the current President was? Or any of his cabinet?

No, but the President wasn't in DC. He was on the oil rig.

Understood. I was hoping to reference him by name, though. Ah well - if it's truly not documented anywhere than I can make up whatever I like.

Yep there are no names. Only names of pre-war government officials I can remember off the top of my head is Senator mentioned from Van Buren who had a bunker constructed. And some generals and what not as mentioned in computers in 3 and NV.