Hello Ali,
The protons in a nucleus have two forces to contend with, the electromagnetic force which is repulsive as you suggest, and also the strong nucleon-nucleon force which is not only attractive but also much stronger than the other. These two forces involve the exchange of photons in the former and exchange of gluons in the latter. In most cases the strong force wins out.
As far as proton-electron attraction goes, they do indeed attract each other and form a stable element, the hydrogen atom.
LeeH
(published on 12/08/2011)
