Washington (CNN) -- Another influential Republican senator on Sunday backed increasing tax revenue as part of a deficit reduction deal, going against a fundamental stance of fiscal conservatives.

Sen. Lindsey Graham of South Carolina said eliminating some tax breaks and subsidies for special interests was one way to tackle expanding deficits.

"No one on the Republican side is going to vote to raise taxes, but I think many of us would look at flattening the tax code, do away with deductions and exemptions and take that revenue to help pay off the debt," Graham told NBC's "Meet the Press."

For example, he called for eliminating the ethanol subsidy "and a bunch of other subsidies that go to a few people" and put the money "back into the federal treasury" for debt reduction.

"That doesn't raise taxes," Graham said, but instead ends the "gravy train" for special interest groups while reducing the national debt.

Graham joined Oklahoma Sen. Tom Coburn, another staunch conservative, in backing increased revenue despite steadfast opposition by anti-tax groups such as Americans for Tax Reform led by influential conservative strategist Grover Norquist.

Norquist's group wants to shrink the size of government and overall government spending, and therefore opposes any tax or revenue increases. Norquist and Coburn have feuded publicly over the issue, which is certain to provoke debate among Republicans in the run-up to the 2012 national election.

However, Graham's stance indicates that more Republicans are willing to go public with support for some form of what Democrats demand as a component of a deficit reduction deal being worked out in bipartisan talks led by Vice President Joe Biden.

A deficit reduction agreement also would include spending cuts in discretionary and military funding and possible reforms to Medicare and Medicaid, the government-run health care programs for the elderly, poor and disabled.

The Biden-led talks are accelerating this week as both parties push to get a deal that will secure congressional support to raise the federal debt ceiling by early August.

The federal government hit its current debt ceiling limit of roughly $14.3 trillion on May 16. Treasury Secretary Tim Geithner has indicated he can keep the country out of default until August 2, but warned of potentially devastating financial consequences after that point unless Congress increases the federal borrowing limit.

Even with movement toward revenue increase in a deficit reduction deal, the Senate's top Republican is trying to put off the tax discussion for now.

"We're really interested in corporate tax reform, for that matter, tax reform across the board," said Senate Minority Leader Mitch McConnell of Kentucky on the CBS program "Face the Nation. "It's very hard ... to deal with a big subject like tax reform within a month. We need to do it. But it's hard to squeeze that into this time limit we have in connection with the deficit. So we need to concentrate on cutting spending."