WASHINGTON — Republicans in both houses of Congress said Wednesday that they wanted to prevent an increase in Social Security payroll taxes that would otherwise occur in January, but they remained far apart from Democrats on the specifics of how to do it.

A small number of Republican lawmakers indicated that they would be open to the idea of raising additional revenues to offset the cost of extending the payroll tax cut, a break in what has been the party’s nearly solid ranks against tax increases.

Senate Republican leaders introduced a bill that would keep the payroll tax rate at its current level for another year. The cost is roughly $120 billion. Senate Republicans would offset most of the cost by freezing the pay of federal employees through 2015 and gradually reducing the federal work force by 10 percent.

In addition, Senate Republican leaders would go after “millionaires and billionaires,” not by raising their taxes but by making them ineligible for unemployment compensation and food stamps and increasing their Medicare premiums. Democrats said that this part of the Republican proposal was not serious, pointing out that high earners were already ineligible to receive food stamps.