WASHINGTON — Unless Congress acts, during the last week of December an estimated 1.3 million people will lose access to an emergency program providing them with additional weeks of jobless benefits. A further 850,000 will be denied benefits in the first quarter of 2014.

Congressional Democrats and the White House, pointing to the sluggish recovery and the still-high jobless rate, are pushing once again to extend the period covered by the unemployment insurance program. But with Congress still far from a budget deal and still struggling to find alternatives to the $1 trillion in long-term cuts known as sequestration, lawmakers say the chances of an extension before Congress adjourns in two weeks are slim.

As a result, one of the largest stimulus measures passed during the recession is likely to come to an end, and jobless workers in many states are likely to receive considerably fewer weeks of benefits.

In all, as many as 4.8 million people could be affected by expiring unemployment benefits through 2014, estimated Gene Sperling, President Obama’s top economic adviser.