I don't think Chris Christie will get a national position if Trump loses. Christie has some skeletons in his closet in New Jersey and I don't think the Republican Party will want him in the limelight especially after some of the negative press about Trump. Despite this, I think Christie will try to push his luck and see where it takes him.
No, Chris Christie has harmed his reputation by aligning with Trump's campaign. Trump is historically unpopular on both sides of the aisle--both Republican and Democratic. If Trump loses the election, many of his high-profile supporters, like Christie, will be tainted by this unpopularity and will pay a political price. Trump supporters' judgment will be, fairly, called into question and other politicians will be reluctant to align themselves for fear of also being indirectly tied to Trump.
Chris Christie was once the darling of the Republican Party but his aggressive nature which has shone out particularly brightly over the past year whether faced with friend or foe has done little to keep him in the hearts of party members. In addition to this, the scandal from the Bridge fiasco is likely to haunt him for a long time which would make him a liability if he had a high national position.
It does not matter who wins the election. Chris Christie will not have a national position of any kind. He has shown repeatedly that he cannot be trusted. He does not play fairly in politics or in business. He is dishonest in what he does and what he says. We don't need someone like him holding national power.