Is it possible for the sun to burn out tomorrow? Why or why not?

It is and isn't possible at the same time.

Explanation:

Stars form when enough hydrogen collects in one place that the sheer gravitational attraction of the mass to itself causes thermonuclear fusion to commence. Unlike a nuclear bomb, the reaction doesn’t last for milliseconds, but for billions of years, as convection currents carry fresh supplies of unfused hydrogen into the reaction zone, and as heavier, already fused material undergoes fusion again, starting a stepladder of elemental construction, building the table of elements from hydrogen up toward iron as far as conditions will allow.  So basically, the sun doesn’t burn all at once for the same reason a candle doesn’t: It relies on convective processes to freshen its fuel supply