Well, the US is not really in the world-conquering business. "World dominating", perhaps, but actually establishing a US-run world government, even with the USSR helping out, is far too much work and would be a terribly messy business.
Now, an informal "keep a global peace" alliance with the Soviets is not inconcievable, _if_ we can find a common threat serious enough, and a more live-and-let live attitude between the US and USSR.
A common problem is not too hard to imagine. Say a more successful Islamic terrorism (successful use of nuclear terrorism vs both the "Greater Satan" and the "Lesser".), leading to a joint US-Soviet occupation of large parts of the middle east. Throw in a China which remains a hard-line Maoist dictatorship (N. Korea in the Large Economy Size), requiring containment and perhaps a joint approach to managing it's likely very messy collapse. Heck, let's throw in Fascist France (Very Bad fallout from the Algerian situation).
The second problem is more serious: an earlier "Detente" may have been possible, if Kruschev had been able to avoid some of his more provocative silliness, and the US had avoided involvement in Vietnam. [1] Some historians argue that there were some hopeful signs near the end of Eisenhower's term in office, before the U-2 incident blew up in everyone's face. But it's hard to see this going very far with the amount of firepower being aimed west and east in the heart of Europe.
The real problem is Eastern Europe. This is going to be a permanent ideological stumbling block, since the Soviet Union cannot pull out without the local regimes collapsing, with the legitimacy of the Soviet government taking a terrible blow, and cannot remain without maintaining governments of a sort highly unpopular to any American who cares anything about democracy (not to mention pissing off every US voter of eastern European descent). Any ideas on this one?
best,
Bruce
[1] Some might argue that it was precisely the shock of the disaster in Vietnam which made OTLs moves towards Detente possible, but a relaxation of the cold war contest based on feelings of weakness after a defeat by a Communist government could never be anything but half-hearted and resentful on the part of the US, especially with Soviet activities in Africa and elsewhere in the 70's. Things would probably have become confrontational with or without the Soviet invasion of Afghanistan.