The plan, which was rejected by Senate Republicans on Tuesday, would have extended a 2-percent payroll tax cut and bought time for working out a full-year renewal.
The House vote kicked the measure back to the Senate, but Senate members have left Washington for the holidays.
Boehner remains insistent on a full-year extension of the existing payroll tax cut before Jan. 1, urging Obama to haul Senate Democrats back to town to talk to his chosen negotiators.
"Let's get this done today," Boehner told Obama, according to a speaker's aide.
But the Senate showed no inclination to return. If a deal can't be worked out by the end of the year, taxes will go up for 160 million Americans on New Year's Day.
Social Security payroll taxes will go up almost $20 a week for a worker making a $50,000 salary - that's $40 less for a typical paycheck or $1,000 over the whole year. Almost 2 million people would lose unemployment benefits as well.
In a moment of political theater, Democrats on Wednesday tried to call up the payroll tax cut extension bill for a vote as the chamber convened for a ceremonial session at which no formal business was scheduled.
But acting speaker Rep. Michael Fitzpatrick, R-Pa., adjourned the chamber and walked out.
"Mr. Speaker, you're walking out. You're walking away just as so many Republicans have walked away from middle-class taxpayers" and others, Rep. Steny Hoyer of Maryland, the No. 2 House Democrat, shouted to an empty chair where the House presiding officer sits.
The Associated Press contributed to this report.