So far, the party has focused its attention on slimming down federal health care, education, science and labor programs, perhaps by billions of dollars. But some Republicans also have pitched a deeper examination of entitlements, which account for much of the government’s annual spending — and reflect some of the greatest looming fiscal challenges facing the United States.

In recent days, a group of GOP lawmakers has called for the creation of special panels that might recommend changes to Social Security and Medicare, which face genuine solvency issues that could result in benefit cuts within the next decade. Others in the party have resurfaced more detailed plans to cut costs, including by raising the Social Security retirement age to 70, targeting younger Americans who have yet to obtain federal benefits.