Story highlights Senate Democrats will introduce their proposal this week

Republicans oppose paying for it with a surtax on millionaires

The payroll tax cut is scheduled to expire at the end of the year

The average family takes home about $1,000 a year because of it

Senate Democrats this week will propose extending the payroll tax cut and imposing a surtax on people earning more than $1 million to pay for it, Sen. Charles Schumer of New York said Sunday.

Appearing on the NBC program "Meet the Press," Schumer said the proposal would be brought up again if Republicans vote it down due to their general opposition to tax increases.

Schumer, a liberal Democrat, predicted it would be difficult for Republicans to vote against a measure that prevents an increased tax burden on middle-class Americans after protecting tax cuts for the wealthy in deficit reduction negotiations.

However, conservative Sen. Jon Kyl, R-Arizona, said the Democratic plan would increase the tax burden of wealthy job creators to pay for something that failed to bring new jobs this year.

"The payroll tax holiday has not stimulated job creation," Kyl said on "Fox News Sunday."

"We don't think that is a good way to do it."

To Democratic Sen. Dick Durbin of Illinois, the GOP stance "defies logic."

"Republicans are walking away from lower- and middle-income families because they don't want to impose a small, small tax on the wealthiest people in America," Durbin said on the same program.

Even anti-tax crusader Grover Norquist, who is credited with pressuring Republicans to oppose increased taxes in any deficit reduction deal, expressed possible support for extending the payroll tax cut.

"I'm not opposed to extending the payroll tax, necessarily," Norquist said on NBC, adding it would be "destructive" to pay for doing so by raising another tax.

At issue is whether to restore the payroll tax to 6.2% on the first $106,800 of wages into Social Security. This year, wage-earners have only been paying 4.2% from a tax break set to expire January 1.

Failing to extend it would amount to raising taxes during a rough economic patch -- something that President Barack Obama would like to avoid.

According to the non-partisan Center on Budget and Policy Priorities, 121 million families have benefited from the tax break, with an increase in take-home pay of $934 for the average worker.

Moody's Analytics estimated in August that letting the tax cut expire would reduce growth by as much as 0.5%. It called extending the cut one of the "most straightforward" ways to "reduce some of the coming fiscal restraint."