Senate Majority Leader Harry Reid on Monday afternoon will offer a new Democratic proposal to expand a payroll-tax cut for employees while tweaking how the bill is paid for in a nod to Republican concerns.

Democrats will scale back a bill rejected in a Senate vote last week by eliminating proposed payroll-tax benefits for employers. The new bill will leave in place a proposal to cut the payroll-tax rate for employees from 4.2 percent to 3.1 percent, a senior Democratic aide said. That will lower the cost of the plan from $265 billion to $180 billion, in an attempt to address GOP concerns about the measure's overall cost, the aide said.

“We do that regrettably,” the staffer said.

Democrats are not including an extension of federal unemployment benefits in the bill, nor a “doc fix” preventing physicians who accept Medicare from taking a pay cut. Because Democrats believe both will be part of a final deal, their exclusion indicates that Reid’s current offer is a negotiating position that Democrats expect Senate Republicans to block.

A GOP leadership aide said that Democrats have not shared their plans' details with Republicans.

Democrats would pay for the new bill through a combination of measures, the senior Democratic aide said.

Democrats would keep a surtax on salaries of more than $1 million a year but cut the 3.25 percent rate they previously proposed about in half. The exact rate was still being worked out.

The new bill would sunset the surtax after 10 years. This attempts to address GOP concerns that the Democratic plan offered a permanent tax increase in exchange for a temporary payroll-tax cut.

Democrats would also borrow from a list of non-health care mandatory savings created during super-committee talks. These ideas, such as cutting farm subsidies, have been on the table since they were identified by a group led by Vice President Joe Biden earlier this year and are viewed as likely bipartisan ways to pay for a final deal on the payroll-tax and unemployment benefits.

Democrats will adopt a proposed offset included in last week’s GOP alternative for extending the current payroll-tax rate for employees: a means test that prevents people who earn a million dollars a year from receiving federal social benefits, such as unemployment benefits and Social Security. Both that provision and the super committee's saving provision could be included in a final deal late this week or next week.

Reid will outline details of the bill at 2 p.m. and planned to start the process of forcing a vote on Monday. A cloture vote on the measure could come on Thursday or Friday, Democrats said.