President Biden and congressional leaders will resume face-to-face talks on Tuesday to avert a government default, with the White House expressing cautious optimism as the contours of a possible deal began to come into focus.

With time running out to strike a deal to raise the debt limit, broad areas of negotiation have emerged, including fixed caps on federal spending, reclaiming unspent funds designated for the Covid-19 emergency, stiffer work requirements for federal benefits and expedited permitting rules for energy projects.

“I remain optimistic because I’m a congenital optimist,” Mr. Biden told reporters on Sunday in Rehoboth Beach, Del. He added, “I really think there’s a desire on their part, as well as ours, to reach an agreement, and I think we’ll be able to do it.”

Still, on Monday, Speaker Kevin McCarthy reiterated that he believed little progress had been made, telling reporters that the two sides remained “far apart” even with a potential default looming. “We have no agreements on anything. That’s why I’m so concerned,” he added.