WASHINGTON — Any extension of this year’s payroll tax cut must be paid for with savings from elsewhere in the budget, House Speaker John Boehner said today.

Boehner’s comment meant that House and Senate Republicans are united in demanding that any eventual measure, which could cost over $100 billion, not add to the federal deficit. It also suggested that President Barack Obama and Congress would have to find mutually acceptable savings before any extension could become law.

The current tax cut expires Jan. 1.

Republicans have previously expressed a willingness to try compromising with Obama on ways to create jobs, including renewing the payroll tax cut. But Boehner stopped short of predicting that the two sides will reach agreement on extending this year’s 2 percent reduction in the 6.2 percent payroll tax that workers pay or enlarging it, as Obama and many Democrats want.

“If in fact we can find common ground on these extensions, I think you can take to the bank the fact that they will be paid for,” Boehner told reporters.

Mirroring Obama’s proposal, Senate Democrats have introduced symbolic legislation extending the reduction for another year and enlarging it to 3.1 percent.

It faces certain defeat because Republicans oppose the way Democrats would pay for it: A permanent 3.25 percent surtax on incomes exceeding $1 million beginning in 2013.

The Democratic bill would also halve the 6.2 percent payroll tax that employers pay on their first $5 million of payroll costs next year. In an effort to encourage hiring, they would also completely eliminate the levy on some payroll increases this year and next.

Obama’s proposal for 2012 would cost an estimated $265 billion. This year’s narrower payroll tax reduction cost an estimated $112 billion.

Senate Minority Leader Mitch McConnell, R-Ky., said Tuesday that Republicans favor simply extending this year’s 2 percent tax cut for workers for another year. Senate Republicans are expected to announce Wednesday how they would pay for it.