When going from sodium to fluorine, both the nuclear charge and the electrons in the outmost shell (i.e. electrons with approximately the same distance from the nucleus on average) increases. These electrons in the same shell are not very efficient in screening each other from the nuclear charge as about 50% of the electrons are farther outside than a given electron under consideration (See Slater's rules: http://en.wikipedia.org/wiki/Slater's_rules). Hence the effective nuclear charge seen by the outmost electrons increases continuously and the electrons become more tightly bound leading to increased electronegativity.
This physical argument forms the basis for the definition of the Allred-Rochow electronegativity scale which correlates well with the Pauli scale: http://en.wikipedia.org/wiki/Electronegativity