WASHINGTON — President Biden offered a series of concessions to try to secure a $1 trillion infrastructure deal with Senate Republicans in an Oval Office meeting this week, narrowing both his spending and tax proposals as negotiations barreled into the final days of what could be an improbable agreement or a blame game that escalates quickly.

A deal still appears to be a long shot, with potential tax increases the biggest hurdle to winning the kind of Republican support that Mr. Biden has said he is seeking. But the continued movement underscored his hopes for a revival of bipartisanship.

The talks are being sustained by a desire among lawmakers in both parties to reach agreement over what has been a longstanding but elusive goal in Congress: repairing and enhancing the country’s network of roads, bridges, water pipes and other physical infrastructure. Both sides are trying to win favor with the moderate congressional Democrats, particularly in the Senate, who will ultimately decide the fate of the president’s $4 trillion economic agenda.