I believe that the possibility of a nuclear attack upon the United States is as high or greater than it has ever been. The threat from the old Soviet Union during the Cold War was massive. A nuclear exchange between the United States and the Soviet Union could have arguably ended human life on this planet. At least set it back 500 to 1000 years. However, at the point where nuclear war was most likely, (during the Cuban missile crisis), the Soviets proved that they wanted to live and let their grandchildren grow up. The Soviets literally 'turned their ships around' and avoided the war. Today, the threat is not nearly as massive, but it actually is more likely to occur.
The threat of a nuclear attack upon the United States is greatest from rouge states or Islamic organizations. North Korea comes to mind first. N. Korea is constantly threatening South Korea and the U.S. North Korea has even launched small scale attacks, the sinking of the S. Korean destroyer a couple of years ago comes to mind. North Korea has said that they will launch a nuclear attack upon the U.S. Because of the sanctions that we are helping to apply. They see this as an act of war. N. Korea just may back up this threat with action, but I believe that this is less likely to happen than a nuclear attack from an Islamic organization that was able to obtain nuclear weapons.
The Islamic threat in some way resembles the threat of Japan back in the 1930's and 1940's. The greatest similarity that I see is the repeated suicide attack. Japan initiated this method of warfare for only the first time in all of recorded history. They did not organize this until later in the war when it was clear that they were losing and it was their best chance. Islamic governance and nationalism has been in a state of decline since the late 17th century. When Israel was formed, this represented a clear and present danger for the simple reason that it is so close to the epic center of Islam: Mecca and Medina. Judea was the first area outside of Saudi Arabia to be overrun by Islam back in the 8th century. These two facts make it imperative that Islam defeat Israel and lift the 'occupation' in order to protect Mecca and Medina. In other words, Judea is similar to the 'inner defense perimeter' that Japan had established. After the fall of Saipan in June 1944, Japan initiated the repeated suicide attack organizations. They were unleashed during the battle for Leyte Gulf the following October. The time frames are different, but after more than 20 years and 4 conventional wars, it became clear that conventional warfare will not dislodge Israel. Islam then initiated a similar desperate reaction beginning around the time of the Munich Olympics in 1972. As with the Japanese attacks, repeated suicide attacks from the Islamic world has continued to increase in intensity and frequency. One major reason is simply because in both cases, they are seen as being much more effective than anything else that is available. Deployment of nuclear weapons would be a natural step to take.
The very fact that repeated suicide attack is being seen today represents the greatest threat to the use of nuclear weapons or any weapon of mass destruction today. The very use of the tactic gave Japan and Islam a strength that they had lost. The loss of life was incidental. The effectiveness of the method was all-important. The mind set in the culture that spawned these two occurrences are similar. This is where the greatest probability of nuclear attack comes in.
It took the first nuclear attack to end the first occurrence of repeated suicide attack in all of man's history. The two are linked together forever. And it makes sense. Nuclear weapons are the ultimate punitive weapon: They do not discriminate. Nuclear weapons kill and destroy everything. The perfect weapon for anyone bent upon killing as many people as possible with little to no regard for the consequences. Any of the organizations that deploy suicide attackers is not going to hesitate to use any nuclear weapons (Or any WMD) that they are able to get their hands on. What is scary is that this is only a matter of WHEN.