Daniel Ellsberg says that the threat wasn't tactical nukes, so much as all-out nuclear war.

"In mid-1961, the only plan the Pentagon actually had for a large conflict with Soviet forces, left over from Eisenhower, was an all-out nuclear attack on the Soviet Union... NATO planning simply wasn't designed- by the nature of the alliance, and by the realities of the situation- for offensive operations into the Warsaw Pact territory... There was, after all, just one way to hold on to West Berlin [in the event of a blockade]... to threaten to carry out our actual Berlin planning... best described by a skeptical Pentagon colleague: 'We send in a series of increasingly larger probes. If they're all stopped, we fire a [nuclear] warning shot. If that doesn't work, we blow up the world.' "

https://books.google.com/books?id=I3gvDwAAQBAJ&lpg=PP1&pg=PT...

And furthermore:

"any conflict pitting US forces against more than several battalions of Soviet troops anywhere in the world- Iran, Korea, the Middle East, Indochina- would lead to instant US strategic attacks on every city and command center in the Soviet Union and China... no alternative plans existed
for a war involving Soviet forces on a level beyond a division or two except for the general war plan. And that lack was by the directive of President Eisenhower, who had decreed that there should be no plans for "limited war" with the Soviet Union, whether nuclear or conventional, under any circumstances, anywhere in the world. This reflected Eisenhower's military judgement that no war between any significant forces of the United States and the Soviet Union could remain limited more than momentarily. Therefore if such a conflict were pending, the United STates should immediately go to an all-out nuclear first strike rather than allow the Soviets to do so... he was convinced that preparation to fight even a limited number of Soviet divisions on the ground, with or without the use of tactical nuclear weapons, would compel an increase in defense spending that would... [cause a ] 'national bankruptcy'.

...

both American and NATO intelligence had produced enormously inflated estimates of Soviet ground strength. For example, they ignored that a Russian division was less than half the size of an American division. Moreover, the supposed number of Soviet divisions was grotesquely overstated. Most of the oft-quoted figure of "175 Soviet divisions" referred to units that existed only on paper, subject to wartime mobilization, or to units that were grossly undermanned and under-equipped, and many that consisted of nothing more than a headquarters staff. Still, matching even the twenty crack Soviet armored divisions deployed in East Germany would legitimize large budgetary Army requests. These, if granted, would come at the direct cost of Air Force and Navy budgets."

https://books.google.com/books?id=I3gvDwAAQBAJ&lpg=PP1&pg=PT...

And indeed it might actually have worked, but would have been a bit of a Pyrric victory, as it would also have destroyed Europe:

"In 1960-61 it was in reality quite possible... that not a single nuclear warhead would land on US territory after such an American first strike... But our Western European allies in NATO would be quickly annihilated twice over: first from the mobile Soviet medium-range missiles and tactical bombers targeted on them... and second from the close-in fallout from our own nuclear strikes on Soviet bloc territory."

https://books.google.com/books?id=I3gvDwAAQBAJ&lpg=PP1&pg=PT...