Two Republican lawmakers on Sunday insisted the GOP should accept President Barack Obama’s offer to extend current rates for a majority – but not all – of taxpayers as part of a compromise to avert the looming fiscal cliff.

Sen. Bob Corker of Tennessee became the second Republican in the upper chamber to signal an openness to raising tax rates, during an appearance on “Fox News Sunday.” Corker, a member of the Senate Banking Committee,  is the latest of a growing group of Republicans who say the GOP caucus should give in to the president and allow the Bush-era tax cuts to expire for the wealthy in January.

"There is a growing group of folks that are looking at this and realizing that we don't have a lot of cards as it relates to the tax issue, before year-end. I mean, we have one house, that's it," Corker said, saying the idea has “merit.”

But Corker said he expected Democrats to compromise and expect spending cuts to social safety net programs such as Medicare.

"The focus then shifts to entitlements, and maybe that puts us in a place where we actually can do something that really saves this nation," Corker said. "I actually am beginning to believe that is the best route for us to take."

Fellow Oklahoma Sen. Tom Coburn, signaled an openness to raising taxes on top earners last week, telling CNN's Erin Burnett he is "OK to compromise on even some of my issues if in fact we'll solve the problem."

Although the Republican-led House has been reluctant to agree to Obama’s demand for higher tax rates on yearly incomes above $250,000, some congressman have defied party leadership to suggest the move is necessary as part of a deficit-reduction package.

Speaking on CNN’s “State of the Union” on Sunday, Rep. Tom Cole once again insisted Republicans should cave to Democrats on the issue. While the Republican congressman said he did not want to see taxes rise, he noted that unless Congress acts fast those rates will automatically increase in a matter of weeks.

“So just let’s make sure for the 98 percent, they know they’re not. We can continue to fight on the other 2 percent and the higher rates,” Cole said, adding that the compromise would give Republicans more leverage in the negotiations to avoid the $7 trillion in tax hikes and spending cuts scheduled to go into effect in January.

Cole was the first senior Republican to urge his party’s leadership to embrace the immediate extension of tax cuts for middle class households, telling the New York Times last month the GOP should leave the fight over the tax rates for the wealthy for another day.

House Speaker John Boehner has adamantly opposed allowing the lower tax rates to expire for the top 2 percent. This week Boehner, in a counteroffer to Obama, proposed raising $800 billion in revenue – just half of what has been suggested by Democrats – by limiting tax deductions and loopholes. The White House, noting the proposal did not specify just which deductions would be limited, immediately rejected the plan.