The payroll tax holiday hasn't done anything to stimulate job growth, so Republicans may not support extending the tax cut favored by President Obama and Democrats -- at least in its current formula -- a key GOP senator said Sunday.

Arizona Sen. Jon Kyl, the No. 2 Republican in the Senate and a member of the failed Super Committee, said Congress is working to address the payroll tax holiday and unemployment benefit extensions before the end of the year when they are set to expire.

But, he said, even though Republicans backed tax breaks under George W. Bush that were not paid for, the payroll tax holiday is a different ball of wax.

"The problem here is that the payroll tax doesn't go into general revenue, it supports Social Security. And you can't keep extending the payroll tax holiday and have a secure Social Security. That's the first problem," Kyl told "Fox News Sunday."

Kyl said the second problem is the effort by Democrats to raise the current tax rate for top earners -- which Democrats argue unfairly favors the wealthiest Americans -- to pay for the payroll tax holiday.

"By taxing the people who provide the jobs, you put off the day we have economic recovery and job creation in this country," Kyl said. "And that's precisely what the Democratic plan would do. It would hit those people, the small businesses who we all acknowledge are the ones who create the jobs coming out of economic difficulty."

Sen. Dick Durbin of Illinois, the second-ranking Democrat in the Senate, said not extending the payroll tax holiday will amount to a tax increase of $1,500 for the average family.

"If we don't provide the tax relief that President Obama has asked for, families are going to see an increase in taxes," said Durbin, who appeared with Kyl. "I can't believe that at a time when working families in this country are struggling paycheck to paycheck, when we need them to have the resources to buy thing in our economy, to create wealth and profitability and more jobs, that the Republican position is, they'll raise the payroll tax on working families? I think that just defies logic."

Some economists argue that failing to extend both the payroll tax cuts and unemployment benefits will cut growth by 1 percent to 2 percent next year and cost more than a half million jobs. Others argue those are bogus numbers.

Sen. Chuck Schumer, D-N.Y., said he finds it difficult to grasp that Republicans would oppose a tax cut.

"They've spent so much time fighting to preserve the Bush tax cuts for the millionaires, it's hard to believe they wouldn't want to preserve a tax cut for the middle class," he told NBC's "Meet the Press."

"I think it's very hard for Republicans to vote against this given their past history of defending the tax cuts for the wealthiest among us. If they don't, if it doesn't pass once, we're going to put it on the floor again and again, and we would be open to other ideas of paying for it if this one fails," he added.

Democrats have contended that Republicans are afraid to raise taxes on high-income Americans because it would violate a no-new taxes pledge proposed by the conservative Americans for Tax Reform, which is led by Grover Norquist.

Norquist, who followed Schumer, said he doesn't oppose extending the payroll tax holiday on its face, as long as it isn't accompanied by additional tax increases. And while he said he could tolerate a short-term measure, the whole point of the plan was that it is supposed to be temporary.

"Obama was the guy who said that this was a tax holiday. Calling it a tax holiday kind of suggests they viewed it as temporary. Holidays aren't permanent," he said.

Norquist added that the reason Republicans are sticking with the pledge -- signed by 236 House lawmakers and 41 senators -- not to raise taxes is not because they are afraid of him -- as Schumer suggested -- but because twice in the last 30 years, they've agreed to raise taxes as long as spending was cut, but spending never was cut.

"The American people aren't falling for that again. We know that if you raise taxes, the politicians in Washington simply spend it. And they can promise anything they want, but Lucy and the football, Charlie Brown isn't going to fall for this again," he said.

"Tax increases are what politicians do rather than reform government."