WASHINGTON—Amid a high-decibel fight over the nation's budget, there is one emerging area of agreement: Both parties appear willing to quietly let a major tax cut expire—a payroll tax break enjoyed by about 122 million people.

Congress, aiming to give wage-earners a few extra dollars in each paycheck, first cut the payroll tax, which funds Social Security, to 4.2% from 6.2%, for the 2011 calendar year.

A Democratic proposal to extend the tax cut for 2012 was the subject of a pitched battle last year before it narrowly passed in December.

This time, the White House isn't pushing for another extension. "That was always intended to be a temporary measure to support job creation and economic growth," Jason Furman, a top White House economic adviser, said recently. "It's not something that we have at this stage called for extending into next year."

Republicans were unenthusiastic about the tax cut to begin with, preferring instead a broad overhaul of the tax code and contending it would weaken Social Security. Now the party is openly opposed to extending the tax break.