WASHINGTON — Bowing under intense pressure from members of their own party, House Republican leaders agreed Thursday to accept a temporary extension of the payroll tax cut, beating a hasty retreat from a showdown that Republicans increasingly saw as a threat to their election opportunities next year.

Under a deal reached between House and Senate leaders, the House will now approve as early as Friday the two-month extension of a payroll tax holiday and unemployment benefits approved by the Senate last Saturday, and the Senate will appoint members of a House-Senate conference committee to negotiate legislation to extend both benefits through 2012.

House Republicans — who rejected an almost identical deal on Tuesday — collapsed under the political rubble that has accumulated over the week, much of it from their own party, worried that the blockade would do serious damage to their appeal to voters.

The House speaker, John A. Boehner, determined to put the issue behind his party, announced the decision over the phone to members on Thursday, and did not permit the usual back and forth that is common on such calls, enraging many of them.