A nuclear attack in the US by an Islamic group made to look like a Soviet sneak attack? Really? Who would buy a Russian attack like that?
A paranoid National Security Adviser having a nervous breakdown and a president that thought he could ignore learning about international affairs, for starters. Also, the Islamic connection was unknown at the NCA level until Clark and Chavez caught Qati and the other guy. All the NCA knew was that they had apparently credible reports of missing nuclear weapons and instability in the Soviet government that threatened to send the country into a civil war. The readers knew neither was actually the case, but the characters didn't, outside of Ryan and a few people who weren't exactly first on the Fowler administration's Christmas card list.
The entire plot is based on the premise of the President not being up to the job; when isolated from all of his competent advisors and left to rely solely on the incompetent one, of course he's going to make a horrible judgement call.
Also, in the book, the bombing of Denver is followed up by a group of the villains starting a conflict between US and Soviet tank divisions on the East/West Germany border. (In the movie, a russian general is bribed to launch an air attack on a US carrier group.) The second attack makes the Americans more likely to believe that the nuclear attack was of Soviet origin.
Movie-related question: Why assassinate the Neo-Nazis, why not just arrest them?
And charge them in what jurisdiction, and with what crime in particular, and how would you sentence them? It's a lot of complications for two countries that just want to heal on and be at peace. It's better for everyone involved for the perpetrators to simply be taken care of.
They've killed at least half a million people. In real-life, I imagine the governments of the world would prefer they be killed.
Also from the movie, how were the neo-nazis suppose to take over? Their plan is get the US and Russia to nuke each other basically, but it forgets the large US military presence in Europe and the fact that most european countries are US allies. The russians would at the very least take these out. Are we to assume that in the post-war chaos they would have all the levers of power given to them? We never really know how they plan to govern a post-war nuclear wasteland that would have been called Europe.
The Neo-Nazis undoubtedly intend to rise in the resulting militaristic and autocratic ruins of the old world. It's not a plan which has to make sense because it's made by a bunch of Neo-Nazis. They're deluded about who, exactly, is going to benefit from their actions.