Negotiations over a last-ditch agreement to head off large tax increases and sweeping spending cuts in the new year appeared to resume Sunday afternoon after Republican senators withdrew their demand that a deal must include a new way of calculating inflation that would lower payments to beneficiaries programs like Social Security and slow their growth.

Senate Republicans emerged from a closed-door meeting to say they agreed with Democrats that the request — which had temporarily brought talks to a standstill — was not appropriate for a quick deal to avert the tax increases and spending cuts starting Jan. 1.

To hold the line against raising taxes on high-income households while fighting for cuts to Social Security was “not a winning hand,” Senator John McCain, Republican of Arizona, said.