US Presidential politics has a thing known as "rally around the flag", a phenomena in which times of crisis is greeted by increased trust in the President. Probably the biggest example of this is when George W Bush jumped from 50% to 90% the day after 9/11. But the same kind of thing has happened with most recent Presidents. It doesn't mean they will win the next election though, or that their approval will last. Carter had a bounce before losing because of the bad economy, Bush Snr had a bounce because of the Gulf War, but lost the election also because of a bad economy. Bush Jnr had a woeful approval rating when his second term ended, which was in the middle of the GFC. Apparently the uptick in Trumps approval isn't all that big compared with past rally around the flag bounces. What Trump and his advisors will be really worried about is the economy, which will be the real factor in his reelection chances. If it tanks, it will make it very tough for him to win again, if history is anything to go by.
Details for the above, and also an interesting finding that such rally around the flag bounces have changed to become very partisan in the Obama-Trump era
can be read in this article.
It is the growing partisanship in politics that underlines what is going wrong in western democracy of late.