WASHINGTON—House Republicans Thursday torpedoed a bill to extend benefits for the long-term unemployed, pressing their demand that the $12 billion cost of continuing the program be offset rather than adding to the deficit.

In a defeat for Democrats trying to keep the program from expiring Nov. 30, the House rejected a bill to continue the program for three more months.

Lawmakers in both parties expect a compromise eventually to be reached—but not until December, after the current program expires. Without an extension, 800,000 unemployed workers will lose their benefits by Nov. 30 and two million by the end of December. A similar lapse in benefits occurred last summer as Congress struggled to break another impasse.

The unemployment aid is just one of many issues before the lame duck Congress that are confounding President Barack Obama and congressional leaders. Others include the fate of the Bush-era tax cuts that are due to expire Dec. 31 and a funding mechanism to keep the government running after a stop-gap appropriations bill expires Dec. 3.