WASHINGTON—Lawmakers worked Sunday to break the impasse that extended the federal government shutdown into a second day, in an effort to prevent it from hardening into a prolonged standoff that could be increasingly difficult to resolve.

A group of centrist senators from both parties huddled in an attempt to chart a way out of the stalemate. As the hours passed, pressure mounted on both parties, with lawmakers aware that the shutdown’s effects would expand as the workweek began, including potential furloughs for tens of thousands of federal employees.

Without an agreement Sunday night, a blame game that Democrats and Republicans carried on all weekend was likely to intensify, lawmakers said.

“I am really worried about where this thing goes because it’s going to get nastier in terms of rhetoric,” said Sen. Lindsey Graham (R., S.C.), predicting it would hit both parties. “First prize in a government shutdown is you get to be dumb, not dumber. That’s the best you can hope for.”

Democrats, who control enough votes in the Senate to block legislation funding the government, have attempted to use their leverage to force an agreement to shield the so-called Dreamers, whose legal protections expire March 5 under President Donald Trump’s decision to end a program called Deferred Action for Childhood Arrivals, or DACA.