Sen Lindsey Graham, R-S.C., told CBS' "Face the Nation" the 2010 Simpson-Bowles plan, which recommends entitlement cuts, was agreeable to him if it also was to the Democrats.
By law, a series of cuts and the end of the George W. Bush-era tax cuts take effect in 2013 unless Congress agrees on deficit reform.
"Mr. President, if you'll say yes to Simpson-Bowles when it comes to revenue, so will I and so will most Republicans," said Graham.
Graham told CBS the GOP remained adamant against raising taxes on any income level; however, ending some unspecified deductions and loopholes on upper-income Americans would generate more revenue for the treasury "without destroying jobs."
At the same, both parties need to get serious about reforming entitlement, Graham said. "We will insist our Democratic friends reform entitlements, something we've never done before," Graham said. "That's where the big money is. Say yes to Simpson-Bowles and we'll get this behind us."
White House adviser David Axelrod said the results of the election confirmed the U.S. public favored having wealthy people pay more in taxes and he was happy to hear encouraging overtures from the GOP leadership about closing loopholes. At the same time, President Obama's re-election proved the voters agreed upper-income Americans could and should chip in more than they already do and that increased revenues were needed to address the budget deficit.
"Every objective person who's looked at this agrees on that so the question is where is that revenue going to come from?" Axelrod asked. "The president believes it's more equitable to get that from the wealthiest Americans who have done very well and frankly don't need those tax cuts."
2014: The Year in Music [PHOTOS]