WASHINGTON - (AP) - House Republicans on Thursday caved to demands by President Barack Obama, congressional Democrats and fellow Republicans for a short-term renewal of payroll tax cuts for all workers. The breakthrough almost certainly spares workers an average $20 a week tax increase Jan. 1. After days of wrangling that even Speaker John Boehner acknowledged "may not have been politically the smartest thing in the world," the Ohio Republican abruptly changed course and dropped demands for immediate holiday season talks with the Senate on a full-year measure that all sides said they want. The House and Senate plan to act on the two-month extension Friday. House Republicans were under fire from their constituents and GOP establishment figures incensed that they would risk losing the tax cut issue to Democrats at the dawn of the 2012 presidential and congressional election year. "In the end House Republicans felt like they were reenacting the Alamo, with no reinforcements and our friends shooting at us," said Rep. Kevin Brady, R-Texas. Boehner said he expects both House and Senate to pass a new bill by Christmas that would renew the tax break while congressional negotiators work out a one-year measure that would also extend jobless benefits for millions of Americans and prevent doctors from absorbing a big cut in Medicare payments. The developments were a clear win for Obama. The payroll tax cut was the centerpiece of his three-month campaign-style drive for jobs legislation that seems to have contributed to an uptick in his poll numbers. "Because of this agreement, every working American will keep his or her tax cut - about $1,000 for the average family," Obama said in a statement. "That's about $40 in every paycheck. And when Congress returns, I urge them to keep working to reach an agreement that will extend this tax cut and unemployment insurance for all of 2012 without drama or delay." If the cuts had expired as scheduled, 160 million workers would have seen a 2 percentage point increase in their Social Security taxes. And up to 2 million people without jobs for six months would start losing unemployment benefits averaging $300 a week.For President Obama's speech on payroll cuts, click on iO Extra on Channel 612.