Speaker Kevin McCarthy’s demand that any deal to raise the debt limit must include stricter work requirements for social safety net programs — and President Biden’s hints that he might be willing to accept such a bargain — has drawn a backlash from liberal Democrats in Congress, underscoring the tricky politics at play in bipartisan talks to avert a default. The proposal has become a central issue in negotiations between Mr. Biden and Mr. McCarthy, which entered a new phase this week as the two offered glimmers of hope that they could reach a deal to increase the borrowing limit, now projected to be reached as early as June 1, and avoid an economic catastrophe. House Republicans’ debt limit bill, approved last month along party lines, would impose stricter work requirements for beneficiaries of food stamps, Medicaid and Temporary Assistance for Needy Families, and the speaker said this week that Republicans would insist on such a provision as part of any deal. Mr. Biden has pointedly left the door open to the idea, noting that he voted for work requirements as a senator. Talk of such a compromise has set off a wave of anger among liberals on Capitol Hill, who have begun openly fretting that the president might agree to a deal they cannot accept.

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