What is left of governments struggle to piece themselves back together (you’d probably see some mixture of military and remaining civilian governments on state/province level having to take over). Years of hardship and rebuilding would take place but with the existential threat of Mars looming, the world may be a bit more unified once the dust settles and rubble cleared. At that point, a fleet of either commandeered or reverse engineered ships would attempt to be assembled to get revenge, bad music in tow.I always wondered what the aftermath of Mars Attacks! would look like.
All of congress is dead, the executive branch wiped out to the point that the daughter of the last president is handing out medals. A whole bunch of Martian ships have crash landed all over the world, with lots of interesting new technology and toys to study. Oh, and apparently aliens can be killed by bad music.