Updated from 4:48 p.m. ET with John Boehner's press conference.

WASHINGTON (

TheStreet

) -- House Speaker John Boehner (R., Ohio) agreed with Sen. Harry Reid (D., Nev.) Thursday to pass the Senate's temporary extension of the payroll tax cut that was set to expire on Dec. 31.

Boehner said the new bill will be approved by the House to reflect the bipartisan agreement in the Senate and that it will allow employers to process and withhold payroll taxation under the same accounting structure currently in place.

"The Senate will join the House in immediately appointing conferees, with instructions to reach agreement in the weeks ahead on a full-year payroll tax extension," Boehner said in a statement. "We will ask the House and Senate to approve this agreement by unanimous consent before Christmas."

Boehner said the bill will ensure that taxes do not increase on working families and that a complex, new reporting burden will not affect small businesses.

In a news conference, a reporter asked if Boehner was certain that a majority of House Republicans would vote to support the bill; the House Speaker said he couldn't say for sure, but that he would do everything to make sure it passes.

"Sometimes it's politically difficult to do the right thing," Boehner said when asked if he thought he had caved on the agreement.

-- Written by Joe Deaux in New York.

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