The USSR posed an existential threat to the United States, especially after it began to deploy ICBMs en masse. There was no reliable way to counter an ICBM strike in the 1960s, and there is still really no good way to do it. Russian ICBMs and SLBMs targeted American and NATO HQs, defense installations, political centers, and industrial regions. A full scale nuclear exchange would have likely destroyed every major city in North America and Europe. So that was a pretty major threat that the US and NATO had to counter.
The Cold War lasted so long because it was a system which fed off of itself, and was supported by a lack of communication between the superpowers. Essentially, the United States and the Soviet Union didnt always talk to each other, and when they did they didnt always tell the truth, or speak from a place of mutual understanding. Rather, the relationship between the countries was based on suspicion, fear, and the mutual belief that the other power was lying. The Soviets and Americans routinely interpreted the others actions as an act of preplanned malice which hoped to embarrass, weaken, or destroy the other. This led to a situation in which both countries antagonized each other, engaged in one-upmanship, and generally acted defensively. These words and actions went to reinforce the whole system, and were proof that the other party was indeed duplicitous. To put it simply, nobody understood each other, or trusted one another, and only expected the worst from their opponents. In this system, there was no true reconciliation. Neither the USSR nor the US were able to discuss the fundamental problems which undermined their relationship.
Trying to figure out what those underlying problems are is another issue. Many during the Cold War argued that the problem was systematic. They said that the Totalitarian Communist USSR held a worldview which was simply incompatible with Democratic Capitalism. As long as Communism existed in the world, Democracy was under threat. To these people, the only way the Cold War could end is if one power defeated another (which was expected to be a bloody prospect). Other point to other causes for the Cold War, including the Russian conquest of Eastern Europe during World War Two and the subsequent domination of that region following the war. For the Soviet's part, many were afraid that the Capitalist countries, and especially Germany, would eventually come to try and finish the job they started in 1941 (or really, 1914). They feared that if they werent firm with the West, that the West would itself act unfaithfully and undermine the USSR.
Im not sure why the Cold War started. Ive done a lot of research on the subject, but I have found no satisfactory answer. Really, I think it is some combination of Russia's actions at the end of World War Two, a European fear of eastern domination, and an intrinsic American fear of the popular power of Communism. But what is undeniable is that these factors all drove a rift between the US and the USSR, and forced them into an existential conflict. The Cold War ended because one power one. We (I) happen to live on the winning side, but its important to remember that one bloc in the struggle collapsed, fell, was destroyed, and completely eviscerated.
In light of these facts, Im not really sure what the US Congress could realistically have done to hasten the end of the Cold War. I personally believe that unreasonable and irrational fear and suspicion drove the Cold War. Had the US been more worried about things at home and less worried about Communism abroad, things may have been radically different. But given the political atmosphere at the time, I think its unreasonable to expect Congress, nor any other branch of government, to act any differently. If we accept that the only viable solution to the Cold War was to destroy the enemy, then the only solution would have been more military confrontations. Of course, a more confrontational military policy would have increased the likelihood of war in Germany, and war in Germany would have made a nuclear exchange almost certain. Had that happened, you and I would not likely be sitting here, on these machines, exchanging these words.