Ok, here's a little scenario..
The last Martians to die did so a couple weeks after the first reports of Martian machines crashing or going out of control came in. The northern Canadian landing, apparently protected from disease by the arctic climate, may have killed themselves rather than die of disease: in any event, the central “nest” was a half-mile wide pool of molten ground when Canadian forces came to investigate.
Recovery began. The US was fairly quick of the mark: although nearly one in ten Americans had died during the invasion, the political system remained intact, and the sheer size of the nation meant large areas remained untouched by the invasion, which had moved outward from the landing sites in a slow and methodical manner, with no long-distance raiding. Martial law was called of after eighteen months, and massive reconstruction loans helped stimulate industry. The most notable social trend was a strong religious revival brought on by the seemingly miraculous nature of humanity’s salvation: one of the scientists involved in the initial struggle became a preacher at the church he and his wife had found refuge in on the day the Martians began to die...
Other areas were less fortunate. Various local strong men arose in Latin America as weak local governments crumbled in the face of the invasion, while much of colonial Africa, the Middle East, and South Asia descended into chaos. In Indo-China, Ho Chi Min emerged from the woods were he had hidden out during the invasion, and took control of the country in the total disorganization of the French colonial forces. In Egypt, the Muslim brotherhood temporarily seized Cairo in the wake of what was clearly SOME kind of divine judgement. As chaos and amine broke out in Western Europe, forces of the far let took control of local governments in France, Italy, Austria. A new civil war broke out in Yugoslavia.
Not that the USSR was in any shape to take advantage of any of this. Only a few years after Hitler, a second invasion of comparably devastating proportions had nearly broken the state. Stalin hadn’t got out of Kursk in time, and within a couple years power had decidedly passed to the one force capable of restoring order, the army. As it was, Marshal Zhukov was hard pressed to restore government control over the Union proper in the post-invasion chaos, let alone Eastern Europe. No, the Poles, Romanians, etc. would have to be let go: people were starving to death at home, and the Soviet Union could not afford to anger the US, which damaged as it was, was still in substantially better shape than the USSR. The Soviet Union would be lucky to avoid collapse, and would take any US help it could get.
Of course, the US was not in any real way ready to provide a post-Martian “Marshall Plan”, nor was any other nation. A few states had not yet felt a Martian attack when the die-off began, but these were all small states: New Zealand, Liberia, Panama... However, there was a recognition that the global disaster required global solutions. At an emergency UN session held in 1951, it was unanimously agreed to create an international relief fund and reconstruction agencies, and to set up the necessary system for a global food bank, special financial cooperative efforts, etc., in a spirit of “all hang together or hang separately.”
Many idealists saw this as the beginnings of a world government: many intellectuals went into high-flung raptures about how the Martians had made us conscious of our common humanity, or, more cynically, on how the existence of a common threat would finally unify mankind. Unfortunately, human beings are rarely so sensible: the major surviving governments were scared badly enough to work together with traditional enemies in case of a future attack, but were no more willing to give up their sovereignty than France had been willing to merge it’s empire with Britain’s in the darkest days of WWII. After all, how could a world government include both democracies and dictatorships such as the USSR and China? And while the necessity of pooling resources and providing mutual assistance to help in economic recovery was widely appreciated, there was no way the wealthier states were going to take input on how to use their $$ from the poor and backward 2/3 of mankind.
So, what emerged by 1954 was something like a combination of NATO and the EC, comprising the US, most of Europe, Australia-NZ, Japan, and the USSR, closely allied militarily and economically linked: a China (and later India) more loosely tied economically, due to backwardness: and an “outer sphere” of poorer nations expected to provide raw materials and perhaps labor to the Planetary Union - for the common good, of course! A shaky and shambolic structure from the start, it never worked very well, and came under increasing internal stresses as time went by and the Martians failed to make a comeback.
At first the US and USSR did not clash. Initial big power muscle actions such as the US’s quiet support for right-wing European governments squashing local communists were politely ignored by the USSR (by 1990 only Italy, Serbia, and Albania still had communist governments west of the USSR), and the US returned the favor for not objecting to the communist takeover of Korea in the chaos following the Martian attacks on Seoul and P’yongYang. The military regime in the USSR increasingly turned to nationalist forces rather than Communist ones for support, and only Mao still stood for the international proletarian revolution, leading to the essential isolation of China for two decades.
However, the system as it was flawed in a number of ways. Nationalist sentiments and suspicions began to undermine the system of international labs and research centers set up to investigate Martian technology, and dragged their heels on turning over all the equipment found to the international commissions. By the mid-70's it was estimated that nearly twice as much was being spent on illegal local, national research programs as was by the official international effort.
Meanwhile, things were not going well in the former colonial territories...