WASHINGTON (AP) — Senate Republicans would probably agree to higher tax rates on the wealthiest Americans if it meant getting a chance to overhaul costly government entitlement programs like Medicare and Social Security, a GOP senator predicted Sunday.

The comments by Bob Corker of Tennessee — a fiscal conservative who has been gaining stature in the Senate as a pragmatic deal broker — puts new pressure on House Speaker John Boehner and other Republican leaders to rethink their long-held assertion that even the very rich shouldn't see their rates go up next year. GOP leaders have argued that the revenue gained by hiking the top two tax rates would be trivial to the deficit, and that any tax hike hurts job creation.

But Corker says insisting on that red line — especially since President Barack Obama won re-election after campaigning on raising tax rates on the wealthy — might not be wise.

"There is a growing group of folks looking at this and realizing that we don't have a lot of cards as it relates to the tax issue before year end," Corker told "Fox News Sunday."

If Republicans agree to Obama's plan to increase rates on the top 2 percent of Americans, Corker added, "the focus then shifts to entitlements and maybe it puts us in a place where we actually can do something that really saves the nation."

Besides getting tax hikes through the Republican-dominated House, Corker's proposal faces another hurdle: Democrats haven't been receptive to GOP proposals on the entitlement programs. Senate Democratic Whip Dick Durbin, D-Ill., on Sunday was skeptical about proposals to increase the eligibility age for Medicare from 65 to 67. He said he doesn't see Congress addressing the complicated issue of Medicare overhaul in the three weeks remaining before the end of the year.