Forever. The obstacles were neither scientific nor engineering per se, but political and psychological. Stalin was incredibly paranoid, and did not trust the scientists. (That is why he put Beria, if anything more paranoid, in charge of the Soviet project.) The only reason he was willing to spend in the way needed to build a bomb was because he was assured it was pretty much guaranteed to work, since the design would be copied directly from the successful American bomb. It’s also probably the only reason anyone clever was willing to work on the Soviet bomb, since failure in Stalin’s regime would’ve meant a one-way trip to the gulag – if you were lucky.
Suppose Stalin had not had a guaranteed working plan in hand in 1944? What would he have done when the bombs went off in 1945? He would certainly have pushed forward Soviet atomic research a little, since the American bombs were impressive. But keep in mind Soviet Russia was unbelievably devastated after the war, and unlike Hitler Stalin was not a believer in superweapons that would Change Everything. His first priority would have had to have been restoring the Soviet industrial plant and sustaining the Red Army as far forward as he could’ve done. As details of the Manhattan Engineering District project leaked out (or were obtained by espionage) one thing that would’ve been clear is the scale of the industrial project. That would have dissuaded Stalin from too much emphasis on his own project, first because of the daunting commitment of resources needed, and secondly because it would have strongly suggested (as was indeed the fact) that the Americans had very few more bombs in reserve. Stalin would’ve had to balance the huge expense necessariy to recreate the MED with what that could buy in terms of conventional weapons in Eastern Europe.
Throw in the fact that Stalin was, by that time, a master at manipulating fairly gullible Western leaders (excepting Churchill, who was rarely fooled by Uncle Joe), and he would’ve already taken the measure of Truman at Potsdam and found the latter an easy mark, as well as timid and untried on the international stage. I think Stalin would’ve pushed the bomb project forward only gently, with minimal resources, while working furiously to rebuild Soviet industry and sustain the Red Army’s conventional strength, and counted on bamboozlement and bluff to keep Truman from pressing the temporary American nuclear advantagement.
He would then have observed the extremely rapid American demobilization, the faintheartedness with respect to Eastern Europe’s occupation by the Red Army – remember, that happened before the Americans knew the Soviets had a bomb (1949) anyway – and then the American refusal to use the bomb in Korea, and I suspect that would have reinforced his confidence that he need not flirt with bankruptcy to duplicate the bomb as fast as possible. We can also imagine that if the Soviets did not have a bomb, the American left would’ve been much more effective in pressing for a moratorium on American nuclear weapons development, or even for some kind of international stewardship (a thing many nuclear scientists and some military leaders openly advocated anyway). Stalin would’ve certainly kept that pot well stirred, e.g. made many noble speeches about how his country would gladly give up its nuclear ambitions in exchange for international guarantees. Imagine how attractive the possibility of keeping the nuclear genie bottled up would’ve been to a war-weary American population.
It gets a little hazy towards the end of Stalin’s life, however. Those who knew him say it was very likely he was planning a war of conquest in Europe, probably to acquire the remainder of Germany, by 1955 at the latest. Would he have done that without a bomb, knowing the Americans had one? Maybe, if he was convinced the American arsenal had atrophied, if there was no means to deliver them to the Motherland (it is not clear American strategic bomber development would have proceeded as fast if there were no nukes to be delivered by them), or if nuclear weapons had gone into the hand of the UN. Or maybe the Soviet nuclear program would’ve delivered a Nagasaki-level bomb by 1955, and he could’ve started the war anyway, in which case some fair chunks of Poland and Germany would probably now be like Chernobyl, with “exclusion zones” around them.
But let us assume Stalin dies on schedule, in 1953, and a Soviet bomb has still not emerged. In that case – I can see Stalin’s successors declining to press the matter forward vigorously. None of them were as interested in full-on military conquest as Stalin, and most were not nearly as paranoid. I can see them accepting American monopoly (well, Anglo-Franco-American triopoly) on the bomb the way they accepted American victory in the race to land on the Moon, so long as the American nuclear program remained fairly low level itself. And I think the American program *would * have remained low level, if not atrophied, in the absence of competition with the Soviets. Look what happend to the American space program after the Soviets quit the race after Apollo 11. Recall that even with a Soviet bomb, the Americans almost didn’t pursue the hydrogen bomb.
