How the US Government would deal with a terrorist nuclear attack

Interesting question.

One can use biographical data to make an estimate.

Example 1. Georgie Bush Senior. 

Example 2. Barack Obama.

Example 3. George Bush Junior.

Example 4. Bill Clinton. 

Example 5. Joe Biden.

Assessment.

1. Bush senior; college educated on his own merits, equivalent in masters in aeronautic as a naval aviator. Combat veteran in the most difficult of aviation specialties. By education and experience became a functioning businessman and capitalist on his own merits. Developed into an administrator and national security specialist. As a national leader developed a penchant for interventionism and was most aggressive in a colonial imperialist sense in defending the Brighton Woods System of international order. 

2. Obama; college educated and possibly one of the most astute exploiters of the Chicago school of politics since Mayor Daley. Equivalent to a doctorate of law and political science in education. Major medical care reform and prevention of another global economic catastrophe descending into effects very similar to the Great Depression as he accomplished; puts him, in my estimate among the greatest of American presidents.  He was a cold pragmatist. He repeatedly ignored the advice of his cowardly and ineffectual vice president and steered a course of cautious and doable economic and political reforms. Very conservative in the "preserving of the social order" sense of the word, he was surprisingly one of the most humanly cruel and yet morally courageous of American presidents reserving unto himself the final word and responsibility on who would be murdered by drone strikes or commando actions based on the best information available. This culminated in the decision to assassinate Osama bin Laden inside Pakistan. Might consider that event as an example of "measured response". Nobody sane messed with him domestically or internationally.     

3. Bush junior; college educated with special advantages and a lot of "tutoring". equivalent to a masters in aeronautics and perhaps a bachelors in business administration. Flew one of the most unstable and fault prone mechanically unreliable of the Century series of USAF fighters. Either he was a much better pilot, more courageous, or too lacking in self preservation to care to master the problem prone F-102. Nothing wrong with his spine of iron. Had help to become "successful" in business. Used family connections to become a part owner of a baseball team and to rise in state and national politics. Had excellent judgement in surrounding himself with enablers and assistants. Example; very powerful and adept vice president, Dick Cheney, was almost a duplicate father figure. Delegated too much and perhaps too trusting. Appeared to have great empathy and was "emotional". Made some fundamental international relations and domestic policy errors that led to the economic collapse at the end of his term. Wrong wars, wrong methods, and wrong goals about sums him up. He could have used Obama's sense of measured judgement and saved the world a lot of grief.

4. Clinton: an equivalent to a doctorate in political science. Rhodes Scholar. Highly intelligent and morally bankrupt. Worked a corrupt state political machine like an amateur saxaphonist. As insidious and self-serving and evil as they come as a human being, this man did "good" only when it served his own personal interests. One recognizes the Aesop's fable about the "birds of a feather"? Look at association and collective actions during his misrule and one can assess the results. Key example; instead of a Marshall plan to restructure the defunct remains of the collapsed soviet empire, the "friends of Bill" descended upon and looted Russia of human talent, and anything portable as IPs or resources not nailed down. He left a mess in the Balkans that persists to this day and failed to finish the job in Iraq that Bush senior never completed. In addition to these failings, he allowed 9-11 to germinate and flower as a conspiracy under his watch. All show and no go, sums up the assessment of this poltroon and buffoon.
       
5. Joe Biden. Fixer and enabler. Never held a real job or did anything on his own in his life. Is a liar and a sneak thief.. Rode other people's coattails up a corrupt state's political machine and "inherited" the presidency as the lesser of two evils. His education path was and is even more nuanced than Bush junior's.  Has a yellow streak that he masks with bombasts and boasts that reminds one of his immediate predecessor. And there is this.

link

It is a partisan American political document peculiar to the Congress, nuanced for strictly political reasons, but one cannot dispute the incidents in the public record and the "appearance" of corruption and conflict of interest. Under British law, there would be prosecutions based on Hunter Biden's laptop contents.

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So... to answer the question, how would Bush junior handle a nuclear terrorist level incident? I think judging from the matrix set above and the range of leadership indices; that are present as comparators; that he falls to the more negative outcome range. He would be "emotional" and not as cautious as his father or Barack Obama.  I expect that unless his advisors reigned him in and corralled his instinctive reactions (As they did in 9-11, which was bad enough to cause concern.), that he might over-react; subsequently go after the wrong objectives and mismanage the outcomes as badly as he historically did 9-11.)  

But then again, Clinton and the current American president would probably do much worse, as they did and do.