Sen. Bob Corker says fellow Republicans in the Senate would probably agree to higher tax rates on the wealthiest Americans if it meant getting a chance to overhaul costly government entitlement programs such as Medicare.

Sen. Bob Corker (R-TN) (Chip Somodevilla/Getty Images)

Corker tells "Fox News Sunday" that a "growing" number or Republicans are realizing they "don't have a lot of cards as it relates to the tax issue" in fiscal cliff negotiations.

Such a compromise would represent some movement in the postelection negotiations between President Barack Obama and congressional Republicans to avert the "fiscal cliff" set to kick in by month's end.

Corker is a solid fiscal conservative and bellwether for what other rank-and-file Republicans might support.

(Copyright 2012 by The Associated Press. All Rights Reserved.)