A deal on Capitol Hill that could cut prescription drug costs for millions of Medicare beneficiaries was cautiously cheered by older Americans and their advocates Thursday even as many worried it might never come to fruition.

The health care and climate agreement struck by Senate Majority Leader Chuck Schumer and Democratic Sen. Joe Manchin includes landmark provisions that could help senior citizens, including a cap on out-of-pocket Medicare drug costs and a requirement that the government negotiate prices on some high-cost drugs.

Some of the issues addressed in the deal have been talked abou...