We study the effect of intersegment interactions on the effective bending and stretching moduli of a semiflexible polymer chain with a finite stretching modulus. For an interaction potential of a screened Debye-Huckel type, renormalization of the stretching modulus is derived on the same level of approximation as the celebrated Odijk-Skolnick-Fixman result for the bending modulus. The presence of mesoscopic intersegment interaction potentials couples the bending and stretching moduli in a manner different from that predicted by the macroscopic elasticity theory. We thus advocate a fundamental change in the perspective regarding the dependence of elastic moduli of a flexible polyelectrolyte on the ionic conditions: stretchability. The theory presented here and its consequences compare favorably with recent experiments on DNA bending and stretching at not too low salt conditions. [S0021-9606(00)50244-X].