If the stars were that close (circa 3000 miles), either we would be burnt to a crisp or we need to rewrite the laws of nuclear physics, which work in lab and on the sun (the strong force would need to be stronger and the weak force would need a longer range, which would play havoc with the universe as we know it).
The gravitational force would need to be stronger and the electromagnetic force weaker.
These adjustments would be needed to balance the much smaller mass of the celestial bodies with their need to generate enough radiation pressure through fusion to balance out the gravitational force. (the extra gravity would be needed in order to keep the stars together, the other forces would need adjusting to increase the rate of fusion)
These adjustments would make the sun burn out in a very short time.
However, if we increased the energy of the proton-proton fusion reaction and decreased the weak interaction, it may also work.
My point?
Neither of these scenarios are observed in the real world.