The superconducting transition temperature of the high-T-c SmO1-xFxFeAs superconductors increases monotonically as the F-doping level x increases to 0.20. High-pressure magnetization experiments reveal a strong sensitivity of T-c to interatomic distances in the underdoped regime (x <= 0.12) with the pressure coefficient of T-c d(ln T-c)/dP being strongly positive, However, as the doping level increases further to x = 0.15, we find that this sensitivity is strongly suppressed and at the same time, d(ln T-c)/dP sharply switches over to assume negative values with T-c decreasing with increasing applied pressure. The aburpt change in the pressure response of the superconducting properties of the SmO1-xFxFeAs phases coincides with the putative existence of a quantum critical point (QCP) near x approximate to 0.14, as proposed by resistivity and Hall effect measurements.