I've been trying to formulate this question for awhile, but since it's Air and Space week I felt compelled to ask now!
Prior to the rise of the ICBM as the main instrument of a hypothetical nuclear exchange between the United States and the Soviet Union, the means by which the Soviet Union would presumably have delivered nuclear weapons to the continental United States was strategic bomber aircraft. Not only was this the underlying logic for the civil defense programs of the 1950’s, but it drove a significant number of defense/military decisions, programs and technologies. To counter this perceived threat, the United States had developed and put in place, by the late 1950’s, multiple early warning radar systems (most importantly the DEW Line in the arctic), nuclear-tipped surface-to-air missiles, supersonic interceptor aircraft armed with nuclear air-to-air rockets, and the SAGE system to coordinate a national response.
The Soviets didn’t detonate their first nuclear weapon until 1949 and didn’t conduct their first air-drop test until 1951. Even if the ability to air-deliver weapons in large numbers occurred soon after (which seems unlikely), the only delivery vehicle immediately available was the Tu-4 – a piston-engined, reverse-engineered copy of the B-29. If the Soviets, in a hypothetical attack, managed reliable refueling operations in the far northern regions of the arctic (which would be difficult, at best), a Tu-4 on a one-way mission still wouldn’t have the range to reach most of the US. Subsequent jet-powered bombers (the Tu-16 and Myasishchev M-4) were similarly range-limited.
Only with the introduction of the iconic Tu-95 in 1956 did the Soviets possess an aircraft with significant range to take off from the Soviet Union and deliver nuclear weapons across the continental US. But by this point, Soviet air crews were facing the defenses I noted above. Add to that, presumably it would take at least a few years (so, into 1958 or even 1959) before Soviet aviation would have had enough aircraft and trained air crews so as to make a mass Tu-95 attack possible.
To me, it seems improbable that, come the late 1950’s, Soviet planners would dedicate a large number of irreplaceable aircraft, aircrews and nuclear weapons to suicidal missions likely doomed for failure somewhere over Canada, particularly when Europe offered so many closer-range and less-defended targets.
So: was the Soviet strategic nuclear bomber threat ever actually a threat?
You have kind of answered your own question here, American rhetoric of a "bomber gap" in the mid-1950s were reacting to a grossly inflated threat. Although manned bombers were the only truly reliable delivery platform for the early years of the Cold War, the Soviet bomber program was plagued by numerous problems and hurdles that degraded the potential of its Long-Range Aviation forces.
Part of the problem for the Soviets was technical. Although the Stalinist aviation industry had poured enormous resources into the development of large aircraft in the 1930s like the Tupolev TB-3, these aircraft were more suited to propaganda parades than frontline aircraft. Soviet manufacturers had enormous difficulty in making these large aircraft globally competitive compared to their Anglo-American rivals. Aircraft like the TB-3 were large and impressive, but seldom had the performance to match the image. Barbarossa forced Soviet industry to focus on tactical airpower rather than resolving the problems of its four-engined bombers and the end of the war forced Soviet industry to play catch-up in this regard. Reverse engineering the Tu-4 helped Soviet industry adjust, as did access during the war to Allied industrial plant, but reverse-engineering exposed some of the deficiencies of Soviet industry. Soviet Plexiglas manufacturing, for example, could not match American quality control standards, and the other problems with Soviet manufacturing led to the Tu-4 being much heavier and less maneuverable than the original. The appearance of the Tu-4 in Soviet skies did encourage fears in the West of one-way atomic missions, but doing so would have been difficult. Although the Tu-4 experience did impart to Soviet industry a number of important lessons for the manufacture of large aircraft, there were still technical hurdles in place. Research at Tupolev's OKB-156 in 1950 hypothesized that the current generation of Soviet jet engines would be unable to meet the needs of an intercontinental bomber. Despite these findings, Myasishchev went forwards with the M-4, which began under 1948's Aircraft 80 program for an intercontinental bomber, which was overweight and unable to meet the range requirements. Concurrent with Myasishchev's development of a jet-bomber, the Tupolev bureau acted on the OKB-156 research to develop a turboprop-powered bomber.
Although both Tupolev and Myasishchev eventually produced aircraft with the range to theoretically bomb the US from Soviet bases, the early-generation Tu-95 and 3M bombers were still beset by technical problems that degraded their effectiveness. The Tu-95's engines proved to be quite temperamental initially and required airbases to complicated warm-up equipment. The 3M resolved some of the earlier issues of the M-4, but it was a costly program and its VD-7 engines were also quite maintenance intensive. These performance factors hindered the deployment of these bombers as advanced bases seldom had the infrastructure to support them.
Plans for the use of these bombers often had to adjust for their shortcomings. Plans in the 1940s called for seizing Alaskan airbases to use as forward airbases for the Tu-4 using amphibious assaults from specialized submarines (Project 621/626). Other plans called for one-way missions, which to be fair, SAC also envisioned for short-ranged aircraft like the B-47. When Khrushchev visited the Myasishchev bureau to see development of the M-4, the bureau showed him an attack profile in which the Eastern seaboard -bound bomber landed in Mexico, which was assumed to be neutral. The Soviet Premier rightly chided the Myasishchev engineers for using such an unsound grasp of geopolitics to cover up the program's failures to meet its range targets. Much more so than SAC, the intercontinental missions for Long-Range Aviation increasingly assumed the character of one-way missions.
The problem Long-Range Aviation had on exercises with both the Tu-95 and M-4 in the mid-1950s speaks not only to the technical problems of the Soviet bomber arm, but also to the Soviet's deficit in both human and infrastructure assets. Unlike the US, a good many of Soviet officers and aircrew of the early Cold War did not have experience flying a long-range bombing campaign. Wartime experience had imparted to the Americans experience that underscored the importance of training, satellite fields, navigational beacons, and a whole host of sundry details that made it possible for SAC to swiftly create a program of nuclear patrols around the USSR. In contrast, Long-Range Aviation practically had to create a program from scratch and had to discover much of the lessons the Americans had already learned. The ergonomics of the early generation bombers left much to be desired. Cabins were painted black, making long-flights difficult, the crew lacked both galley and toilet facilities, another problem for an intercontinental bomber. The Soviets experimented with ice-fields as a form of improvised airstrip, but were never really able to overcome the problems inherent to this system. Long-Range Aviation had more success with experiments in air-to-air refueling and it allowed for the Tu-4 and M-4 aircraft to retain some utility as tankers, but Soviet air-to-air refueling never developed the same level of proficiency as SAC.
There were also significant institutional barriers that hindered the development of Long-Range Aviation. The Red Army had gained a significant amount of prestige and clout because of its victory over the Germans and as such, it sought to claim responsibility over nuclear weapons. Since Soviet development of missiles fell under the Army's GAU (Main Artillery Directorate), the rockets as an alternative delivery system found itself a very powerful patron within the Soviet system. Additionally, the initial Soviets were extremely concerned during the Stalinist period of a rogue launch of nuclear weapons by a disaffected officer against the state, so they enacted a cumbersome serious of negative controls for nuclear weapons. Until 1959, Long-Range Aviation bomb storage had their bombs controlled by KGB troops and the process for getting the bombs from their bunkers to the bombers was laborious. Thus nuclear alert meant a very different experience for a Soviet crew than their American counterpart. While SAC's planes flew with operational bombs, their Soviet analogues seldom did. Soviet training was seldom with actual bombs, and alert usually meant sitting on the tarmac. Thus Long-Range Aviation was nowhere near as flexible a force as SAC in the 1950s.
The irony was that Khrushchev's own "New Look" for the Soviet military siphoned off considerable resources from Long-Range Aviation in the early 1960s just as Soviet designers had resolved some of the technical bugs that plagued the force in the 1950s. But the reorientation of Soviet strategic forces towards rockets was in many ways a much sounder strategic choice. All of the problems of Long-Range Aviation had rendered it a reactive force, which ceded initiative to NATO and the Americans and provided little in the way of a second-strike capability. Negative controls for rockets did not degrade their performance as much as manned bombers and likewise did not require a massive base infrastructure for operations against the US. The scare of the bomber-gap had also fostered a beefing up of North American defenses that made the possibility that the bombers could reach their targets a much more distant possibility.
Cruise missiles seemed to offer a way out of this impasse, but the advent of cruise missiles pulled Long-Range Aviation into many different directions. Attacking NATO convoys and surface task forces at sea became one of the emerging raison d'être of the bomber fleet. The emergence of NATO nuclear powers as well as the Sino-Soviet split also fostered a reorientation of the Soviet bomber forces into a continental asset with the Tu-22M emerging as the main platform for these duties. Plans to use bombers against the mainland US atrophied and planned replacement programs for the intercontinental Tu-95 suffered from a pattern of fits and starts during the Brezhnev years. Of the Soviet strategic triad, the manned bomber remained the weakest in the latter Cold War period as the Soviet bomber force began to be pulled into many different strategic directions from the mid-1960s onwards.
The alarmism of the Bomber Gap rhetoric in hindsight comes across as very over-blown and hyperbolic. However, in defense of US commentators, the problems the Long-Range Aviation faced in the 1950s were not insurmountable and both Soviet industry and Long-Range Aviation were aware of them and tried to implement solutions. The problem was one of timing and by the time resolving these technical and infrastructural problems appeared to be in sight, rockets were merging as a viable alternative to the manned bomber. Unlike SAC, Long-Range Aviation lacked the political and institutional clout to keep its position within Soviet nuclear forces and became a nuclear auxiliary rather than a vital component for Soviet nuclear strategy.
Sources
Podvig, P. L., and Oleg Bukharin. Russian Strategic Nuclear Forces. Cambridge, Mass: MIT Press, 2001.
Zaloga, Steve. The Kremlin's Nuclear Sword: The Rise and Fall of Russia's Strategic Nuclear Forces, 1945-2000. Washington: Smithsonian Institution Press, 2002.