The reason we did not "threaten war" is because we didn't have the ability to intervene militarily. However, we provided other kinds of support to the opposition, much of it covert and also rhetorically. We provided the hope that kept the opposition alive. We had a containment policy, the Truman Doctrine, JFK's rhetorical defense of freedom throughout the world, and Reagan's evil empire along with a Polish Pope.
America used the VOA and other ways to communicate with the oppressed in these countries. In short, we had American leaders who could articulate the ideological struggle we were waging.
People forget that the Warsaw Pact had 6,000,000 men under arms and was designed as an unstoppable attack force designed to take Europe within weeks, and that WWIII was expected to end life as we know it, and possibly all human life on the planet.
Today, most of the Warsaw pact is part of our NATO, Russia is alone, and the Russian empire doesn’t exist anymore, yet.