WASHINGTON — A Republican senator said Sunday “it’s fair to ask my party to put revenue on the table” as part of the solution to avoid the looming automatic tax increases and across-the-board spending cuts known as the “fiscal cliff.”

South Carolina’s Lindsey Graham said he’s “willing to generate revenue” by steps such as capping tax deductions, which he says would most affect upper-income Americans. But he says he won’t agree to higher taxes - a position shared by most Republicans in Congress.

President Barack Obama wants to let tax rates rise for individuals earning more than $200,000 a year and married couples earning more than $250,000.

Sen. John McCain, R-Ariz., also expressed a preference to raise federal tax revenue by limiting deductions rather than by raising tax rates.

“I would be very much opposed to raising tax rates, but I do believe that we can close a lot of loopholes,” he said on Fox News Sunday.

But Sen. Dick Durbin of Illinois, the second-ranking Democrat in the chamber, said any deal to reduce budget deficits should include tax increases on upper-income taxpayers.

“Let the rates go up to 39 percent. Let us also take a look at the deductions. Let’s make sure that revenue is an integral part of deficit reduction,” Durbin said on ABC’s This Week.

Obama and congressional leaders are trying to find a compromise in the next few weeks to avert the fiscal cliff, which would trigger $607 billion in tax increases and spending cuts beginning in January.

The Congressional Budget Office has said a failure to avoid the fiscal cliff could lead to a recession and a jobless rate of about 9 percent, compared with the October rate of 7.9 percent. Federal Reserve Chairman Ben Bernanke said last week that a failure to avoid the fiscal cliff would pose a “substantial threat” to the economic recovery.

Business leaders have warned that the fiscal cliff creates uncertainty for consumers and employers.

“There’s a great uncertainty that’s just hanging over the entire economy because we’re not confident” that Congress “can govern anymore,” David Cote, chief executive officer of Honeywell International Inc., said on NBC’s Meet the Press.

“There’s a lot of money on the sidelines that people are willing to invest,” Cote said. “People like me just aren’t hiring now because we’re not confident they can do it.”

The spending cuts are evenly divided between domestic and military spending. The tax cuts, enacted under President George W. Bush in 2001 and 2003, expire at the end of the year.

U.S. stocks had their biggest rally since June last week amid optimism that Obama and Republicans can reach a deal.

The markets “should be optimistic, because we can solve this problem,” Durbin said.

Obama won re-election Nov. 6 on a platform that included higher rates for upper-income taxpayers. Obama wants to extend the Bush-era tax cuts for most taxpayers, while letting them expire for individual income of more than $200,000 a year and married couples’ income over $250,000.

The Democratic-controlled Senate in July passed a bill containing those provisions. The Republican-led House opposes it.

Republicans, who also lost ground in the Senate and House in the elections, generally support extending the Bush-era tax cuts for all income levels. They say Obama needs to show more leadership on curbing spending including on entitlement programs.

Even as Republicans oppose raising tax rates, some have distanced themselves from a pledge they made with the group Americans for Tax Reform to oppose all tax increases and to use any revenue from limiting tax breaks to reduce tax rates.

Graham told ABC’s This Week that he “will violate the pledge, long story short, for the good of the country, only if Democrats will do entitlement reform.”

Rep. Peter King, R-N.Y., said a pledge signed years ago should not necessarily apply in economic conditions that have changed greatly.

“I think everything should be on the table,” he said, adding, “I’m just saying we should not be taking ironclad positions.”

King said on NBC’s Meet the Press that “we have to show the world we’re adults. The election’s over.”

It’s time to get Obama and the congressional leaders in a room to negotiate, he said. “That’s what representative government should be about.No one gets all their way.” Information for this article was contributed by staff members of The Associated Press and by Greg Giroux and Timothy R. Homan of Bloomberg News.

Front Section, Pages 1 on 11/26/2012