Lawmakers seem interested in passing on discounts directly to consumers at the pharmacy counter and changing up how doctors are paid in Medicare as possible legislative solutions to high drug costs.

The Senate Finance Committee held its first hearing on rising drug prices Jan. 29, where witnesses floated possible policy changes before lawmakers on how to best lower drug costs for American patients. The hearing is part of lawmakers’ larger efforts to rein in drugmakers and other entities within the drug supply chain.

One suggestion to lower costs that seemed to resonate with members of the committee, particularly Republicans, revolved...